What is the Least Common Multiple of 870 and 890?

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 890 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 890, than apply into the LCM equation.

GCF(870,890) = 10
LCM(870,890) = ( 870 × 890) / 10
LCM(870,890) = 774300 / 10
LCM(870,890) = 77430

Least Common Multiple (LCM) of 870 and 890 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 870 and 890. First we will calculate the prime factors of 870 and 890.

Prime Factorization of 870

Prime Factorization of 890

Now multiplying the highest exponent prime factors to calculate the LCM of 870 and 890.

LCM(870,890) = 2¹ × 3¹ × 5¹ × 29¹ × 89¹
LCM(870,890) = 77430