Solution - Least common multiple (LCM) by prime factorization

The prime factors of 10,584 are 2, 2, 2, 3, 3, 3, 7 and 7.

The prime factors of 70,560 are 2, 2, 2, 2, 2, 3, 3, 5, 7 and 7.

The prime factors of 134,946 are 2, 3, 3, 3, 3, 7, 7 and 17.

The prime factors of 1,764 are 2, 2, 3, 3, 7 and 7.

Determine the maximum number of times each prime factor (2, 3, 5, 7, 17) occurs in the factorization of the given numbers:

The prime factors 5 and 17 occur one time, while 2, 3 and 7 occur more than once.

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

LCM = $$2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 3\cdot 3\cdot 5\cdot 7\cdot 7\cdot 17$$

LCM = $$2^5\cdot 3^4\cdot 5\cdot 7^2\cdot 17$$

LCM = 10,795,680

The least common multiple of 2,160, 10,584, 70,560, 134,946 and 1,764 is 10,795,680.