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The LCM of two numbers is the product of the numbers if one of the numbers is a prime. Since 11 is a prime, the LCM of 10 and 11 is 110 (10 x 11). If neither number had been a prime, the LCM would have been the product of all the prime factors of the numbers to their greatest power.
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There are no two numbers whose product is 23 and whose sum is 10. 23 is a prime number, and the only numbers whose product is 23 are 23 and 1. A prime number can only be divided by itself and 1.
what is 1450 as a product of its prime numbers