Question 1 Playing with numbers Exercise 2.10 Next
Answer:
Prime factorization of 24 = 2 × 2 × 2 × 3 36 = 2 × 2 × 3 × 3 54 = 2 × 3 × 3 × 3 So the required LCM = 2 × 2 × 2 × 3 × 3 × 3 = 216 The smallest number which is exactly divisible by 24, 36 and 54 is 216 In order to get remainder as 5 Required smallest number = 216 + 5 = 221 Therefore, the smallest number which when divided by 24, 26 and 54 gives a remainder of 5 each time is 221.
Video transcript "Welcome to lido homework. My name is leonie Rolla and in today's Q&A video. We are going to solve a word problem. So let us repeat the question together. What is the smallest number which when divided by 24 36 and 54 gives a remainder of 5 each time. So as you can see that in the question, we are supposed to find s smallest number and that smallest number should be common right foot. Before 36 and 54 in what way says in such a way that whenever we divide that number by 24 we divide that number by 36 and we divide that number by 50 for we should get a remainder of 5 each time. So let us think about it, right? How can we do this? So before I start finding that number for who's the remainder after dividing by 24 36 54 we get the remainder as 5 let us And a number that is divisible by 24 by 36 by 54 right? In fact, let us find the least common number that is or least common multiple of 24 36 and 54. So right now what I'm going to do is I'm going to find the LCM of 24 36 and 54. Let us see how we can do that. So 24 the prime factorization of 24 is as follows 212 size twenty four to six Squeals to these ice 6 similarly for 36 it is going to be to 80s is thirty six to nine size 1833 size 9 similarly for 54 2 to the 4 to 7 of 14 three nines ice 27 3 3 0 is 9 therefore 24 can be written as 2 into 2 into 2 into 3. Similarly 36 can be written as 2 into 2 2 into 3 into 3 and few to 4 can be written as 2 into 3 into 3 into 3, right? Let us first find what are the comments here? So we have two two two common and we have three three three common and it has we have three and three common in the second number and the first and second number. We have two common. Therefore. The LCM e is 2/3 This to this tree and the leftovers in the first case that is two in the second case the third case that is three, right? So let us try to multiply this and see how much we will get to these I-66 to size 12 12 into 3 is 36 their son into here, right? So till here it is 36 and 2 into 3 is 6 now, let us see how we can find the value of 36 into 6. So 6 is 6 3 9 6 3 is 18 216 there for two and six is the least common multiple for 24 36 and 54. But the question is not asking us to find the least common multiple. In fact, the question is asking us to find the smallest number the least number which when divided by 24 36 and 54 which will give me five. Now if I divide 2 and 6 by 24 I'm going to get the remainder is 0 similarly if I divide 2 and 6 by 36 I'm going to get the remainder is 0 and also if I divide 216 by 51, I'm going to get the remainder as 0 right. So now what am I supposed to do so that I'll get the remainder as five. My load sticks tells me that I just need to add 5 to 216 which will give me 2 to 1 therefore if I divide 2 to 1 by 24, I'll get the remainder as five. Strangest chicken legs two to one. Let us try to divide it by 24 so we can know that 24 how many times will give me 2 to 1 any idea there is none, right? So let us find just next to that let us find the multiple of 20 for this next 2 to 21 and it will give me it might be to the 6 from here. Also. I can find it very easily to the for photos of eight a tree size 24. They did you guess so if I divide. Let's say Let's Take by 9:00. Okay, 9:00 for size 36 399 to jst in 216 Creek. So if I multiply 24 into 9, I will get it as 216 and I'm getting the remainder is 5 isn't it similarly when I divide 2 to 1 by 36 and when I divide 54 by 3054 221 by 54R still get the remainder is 5 and that is what the question is asking us. Hence now. Now we can conclude that. Hence. 221 is the required smallest number, right? It is the required smallest number. That's it. So what is the Mercury since this is a word problem. You have to give the answer in terms of statements as well. Okay you to give the answer in terms of statement only. Okay guys, that's it for today's Q&A video. If there is any doubt, please do comment below and if you liked the video and for such upcoming videos to subscribe to Lido "
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Highest common factor : If there are three numbers like 10, 20, 30 and there exists numbers that can divide them to give remainder 0 viz. 5, 10. Then the lowest of those numbers is the HCF viz. 5 Least Common multiple: If we take 4,6 as two numbers then both of them divide 12,
24, 36 etc fully giving remainder 0 so the lowest such
number common to both is the LCM which in this case is 12. Method 1: Method 2: Questions: Q. What is the least number of cans needs for a vendor who has 21 L of Milk 'a' , 42 L of milk 'b' and 63L of Milk 'c'. If all cans should have same number of milk and he should need least number of cans. Ans: Find HCF of 21, 42, 63 which is 21. So total cans are 6 i.e. 1 for milk 'a' , 2 for milk 'b' and 3 for milk 'c'. Q. If the HCF and LCM of two numbers is 18, 180 and one of the number is 36. Then the second number is. Ans. HCF * LCM = a * but HCF = 18, LCM = 180 and a= 36 so substituting we get b = 90. Formulae of HCF and LCM
Q. Find the HCF of (3125 – 1) and (335 – 1).
Ans . 35 – 1
Q. The smallest square number, which is exactly divisible by 2, 3, 4, – 9, 6, 18, 36 and 60, is
Ans . 900
Q. HCF of \( 2^3 * 3^3 * 5 * 7^4 , 2^2 * 3^5 * 5^2 * 7^3 , 2^3 * 5^3 * 7^2\)
Ans . 980
Q. If two given numbers are divisible by a number, then their difference is also divisible by that number.
Ans . true
Q. Two tankers contain 850 litres and 680 litres of kerosene oil respectively. Find the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times
Ans . 170
Q. . In a morning walk, three persons step off together. Their steps measure 80 cm, 85 cm and 90 cm respectively . What is the minimum distance each should walk so that all can cover the same distance in complete steps?
Ans . 12240
Q. Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case.
Ans . 151
Q. Renu purchases two bags of fertiliser of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertiliser exact number of times.
Ans . 3
Q. Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can cover the distance in complete steps?
Ans . 6930
Q. The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.?
Ans . 75
Q. Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12. ?
Ans . 120
Q. Determine the greatest 3-digit number exactly divisible by 8, 10 and 12. ?
Ans . 960
Q. The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again? ?
Ans .
Q. Three tankers contain 403 litres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of the three containers exact number of times.
Ans . 31
Q. Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case
Ans . 95
Q. Find the smallest 4-digit number which is divisible by 18, 24 and 32.
Ans . 1152
Q. Find the H.C.F. of 108, 288 and 360
Ans . 36
Q. Find the H.C.F. of 513, 1134 and 1215
Ans . 27
Q. Reduce \( \frac{391}{667} \) to lowest terms.
Ans . 17/29
Q. Find the LCM of \( 2^2 * 3^3 * 5 * 7^2, 2^3 * 3^2 * 5^2 * 7^4, 2 * 3 * 5^3 * 7 * 11 \)
Ans . 23 * 33 * 53 * 74 * 11
Q. Find the L.C.M. of 72, 108 and 2100
Ans . 37800
Q. Find the L.C.M. of 16, 24, 36 and 54
Ans . 432
Q. Find the H.C.F. and L.C.M. of \( \frac{2}{3}, \frac{8}{9}, \frac{16}{81}, \frac{10}{27} \)
Ans . 2/81 and 80/3
Q. Find the H.C.F. and L.C.M. of 0.63, 1.05 and 2.1.
Ans . 0.21 and 6.30
Q. Two numbers are in the ratio of 15:11. If their H.C.F. is 13, find the numbers.
Ans . 195 and 143
Q. The H.C.F. of two numbers is 11 and their L.C.M. is 693. If one of the numbers is 77, find the other
Ans . 99
Q. Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm
Ans . 45
Q. Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.
Ans .
Q. Find the largest number which divides 62, 132 and 237 to leave the same remainder in each case.
Ans . 35
Q. Find the least number exactly divisible by 12,15,20,27.
Ans . 540
Q. Find the least number which when divided by 6,7,8,9, and 12 leave the same remainder 1 each case
Ans . 505
Q. Find the largest number of four digits exactly divisible by 12,15,18 and 27
Ans . 9720
Q. Find the smallest number of five digits exactly divisible by 16,24,36 and 54.
Ans . 10368
Q. Find the least number which when divided by 20,25,35 and 40 leaves remainders 14,19,29 and 34 respectively.
Ans . 1394
Q. Find the least number which when divided by 5,6,7, and 8 leaves a remainder 3, but when divided by 9 leaves no remainder
Ans . 1683
Q. The traffic lights at three different road crossings change after every 48 sec., 72 sec and 108 sec.respectively .If they all change simultaneously at 8:20:00 hours,then at what time they again change simultaneously .
Ans . 8:27:12
Q. Arrange the fractions \( \frac{17}{18} , \frac{31}{36} , \frac{43}{45} , \frac{59}{60} \) in the ascending order
Ans . 31/36 , 17/18, 43/45, 59/60
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