Solution - Least common multiple (LCM) by prime factorization

The prime factors of 23,456 are 2, 2, 2, 2, 2 and 733.

The prime factors of 34,567 are 13 and 2,659.

The prime factors of 45,678 are 2, 3, 23 and 331.

The prime factors of 56,789 are 109 and 521.

Determine the maximum number of times each prime factor (2, 3, 5, 13, 23, 109, 331, 521, 733, 823, 2,659) occurs in the factorization of the given numbers:

The prime factors 3, 5, 13, 23, 109, 331, 521, 733, 823 and 2,659 occur one time, while 2 occurs more than once.

The least common multiple is the product of all factors in the greatest number of their occurrence.

LCM = $$2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 5\cdot 13\cdot 23\cdot 109\cdot 331\cdot 521\cdot 733\cdot 823\cdot 2659$$

LCM = $$2^5\cdot 3\cdot 5\cdot 13\cdot 23\cdot 109\cdot 331\cdot 521\cdot 733\cdot 823\cdot 2659$$

LCM = -7587376677960587680

The least common multiple of 12,345, 23,456, 34,567, 45,678 and 56,789 is -7587376677960587680.