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If the least common multiple of two numbers equals the product of the two numbers, then the numbers are relatively prime, that is their highest common factor is 1.

For example, the numbers 10 and 21:

The lcm is 10 x 21 = 210

They are relatively prime since their hcf is 1.

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Q: What least common multiple equals the product of the two numbers?
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Why is the least common multiple of 2 prime numbers their product?

Because prime numbers don't have any common prime factors. Their GCF is 1. Since the product of the GCF and LCM of a pair of numbers equals the product of the numbers, the LCM has to be equal to the product.


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What is the least common multiple of 49 and 343?

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