What is the Least Common Multiple of 870 and 880?

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 870 and 880 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 870 and 880, than apply into the LCM equation.

GCF(870,880) = 10
LCM(870,880) = ( 870 × 880) / 10
LCM(870,880) = 765600 / 10
LCM(870,880) = 76560

Least Common Multiple (LCM) of 870 and 880 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 870 and 880. First we will calculate the prime factors of 870 and 880.

Prime Factorization of 870

Prime Factorization of 880

Now multiplying the highest exponent prime factors to calculate the LCM of 870 and 880.

LCM(870,880) = 2⁴ × 3¹ × 5¹ × 29¹ × 11¹
LCM(870,880) = 76560