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### Question: Which of the following is the multiple of 8? 72, 98, 106, 124, 164 ### Answer: 72 is divisible by 8 98 is not divisible by 8 106 is not divisible by 8 124 is not divisible by 8 164 is not divisible by 8 so the answer is 72,

### Question: Find the sum of all the multiples of 7 between 50 and 80 ### Answer: The numbers divisble by 7 between 50 and 80 are 56, 63, 70, 77. So the sum of these numbers 56+63+70+77 = 266,

### Question: Write the prime factors of 35 and express the answer in this form 2.3.3 ### Answer: The factor pair of 35 is 5 and 7. Since both are prime numbers the answer is 5.7,

### Question: Find the prime factorization of 36 and express the answer in this sample form 2.3.3 ### Answer: We can start with any factor pair such as 3 and 12, we write 3 and 12. The factor 3 is prime whereas factor 12 is composite so we need to find its factors. Lets take 3 and 4 as factors of 12. Here 3 is a prime number and 4 is composite. So we need to find its factors The factors of 4 is 2 and 2. 2 is a prime number Now, writing down prime factors in ascending order we get 2.2.3.3,

### Question: Find the least common multiple of 2 and 4 s by listing multiples. ### Answer: Multiples of 4 = 4, 8, 12, 16, 24,… Multiples of 2 = 2, 4, 6, 8, 10,… The smallest number to appear on both lists is 4 so the least common multiple is 4 So LCM of 2 and 4 is 4,

### Question: If x is the least common multiple of 8 and 9 found by listing mulitples then find x ### Answer: Multiples of 8 = 8, 16, 24,32, 40, 48, 56, 64, 72, 80,… Multiples of 9 = 9,18, 27, 36, 45, 54, 63, 72, 81, 90… The smallest number to appear on both lists is 72 so the value x is 72,

### Question: Find the least common multiple of 60 and 315 by prime factorization method ### Answer: Prime factors of 60 = 2x2x3x5 Prime factors of 315 = 3x3x5x7 Bringing down the primes in each column we get 2x2x3x3x5x7 = 1260 so the answer is 1260,

### Question:  Find the lowest number which is exactly divisible by 18 and 24 ### Answer: Prime factors of 18 = 2x3x3 Prime factors of 24 = 2x2x2x3 Bringing down the primes in each column we get 2x2x2x3x3= 72 so the lowest number which is exactly divisible by 18 and 24 is 72,

### Question: A shopkeeper sells candles in packets of 12 and candle stands in packet of 8. What is the least number of candles and candle stands Nita should buy so that there will be one candle for each candle stand ### Answer: To find a quantity which is the lowest common multiple of different quantities, we find the LCM. Multiples of 12 are 12, 24, 36, 48, …… Multiples of 8 are 8, 16, 24, 32, 40, …… The lowest common multiple is 24. So, the least number of candles and candle stand that Nita should buy is 24.,

### Question: A cinema runs its movies in two different halls 24/7. One movie runs for 80 minutes and the second one runs for 120 minutes. Both movies start at 1.00 p.m. When will the movies begin again at the same time? ### Answer: we express 80 and 120 as product of their prime factors 80 = 2x2x2x2x5 120=2x2x2x3x5 LCM of 80 and 120 = 2x2x2x2x5x3 = 240 so the two movies will start again at the same time after 240 minutes, that is in 4 hours The movie will again start at 5.00 pm,