Factor into powers of primes
45 = 3²·5
105 = 3·5·7
200 = 2³·5²
LCM = 2³·3²·5²·7 = 12,600
45 = 3²·5
105 = 3·5·7
200 = 2³·5²
LCM = 2³·3²·5²·7 = 12,600
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You are looking for the smallest number that has 200, 105 and 45 as factors. To do this, find the prime factorization of the 3 numbers
45 = 3 * 3 * 5
105 = 3 * 5 * 7
200 = 2 * 2 * 2 * 5 * 5
The least common multiply must contain all the factors of each number with as little extra as possible
2 * 2 * 2 * 3 * 3 * 5 * 5 * 7 = 12,600
You can prove this to yourself by removing each factor in turn. you will find that if any of them are removed, the number will no longer be divisible by all the above numbers.
45 = 3 * 3 * 5
105 = 3 * 5 * 7
200 = 2 * 2 * 2 * 5 * 5
The least common multiply must contain all the factors of each number with as little extra as possible
2 * 2 * 2 * 3 * 3 * 5 * 5 * 7 = 12,600
You can prove this to yourself by removing each factor in turn. you will find that if any of them are removed, the number will no longer be divisible by all the above numbers.
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lcm is 5 since they are all multiples of 5 divide them with 5 . It gives 9,21,and 40 There is no common number that divides 9,21, and 40.
So LCM is 5
So LCM is 5
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12,600