What is the Least Common Multiple of 69552 and 69570?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 69552 and 69570 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69552 and 69570, than apply into the LCM equation.

GCF(69552,69570) = 18
LCM(69552,69570) = ( 69552 × 69570) / 18
LCM(69552,69570) = 4838732640 / 18
LCM(69552,69570) = 268818480

Least Common Multiple (LCM) of 69552 and 69570 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69552 and 69570. First we will calculate the prime factors of 69552 and 69570.

Prime Factorization of 69552

Prime Factorization of 69570

Now multiplying the highest exponent prime factors to calculate the LCM of 69552 and 69570.

LCM(69552,69570) = 2⁴ × 3³ × 7¹ × 23¹ × 5¹ × 773¹
LCM(69552,69570) = 268818480