What is the Least Common Multiple of 10656 and 10670?

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 10656 and 10670 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10656 and 10670, than apply into the LCM equation.

GCF(10656,10670) = 2
LCM(10656,10670) = ( 10656 × 10670) / 2
LCM(10656,10670) = 113699520 / 2
LCM(10656,10670) = 56849760

Least Common Multiple (LCM) of 10656 and 10670 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10656 and 10670. First we will calculate the prime factors of 10656 and 10670.

Prime Factorization of 10656

Prime Factorization of 10670

Now multiplying the highest exponent prime factors to calculate the LCM of 10656 and 10670.

LCM(10656,10670) = 2⁵ × 3² × 37¹ × 5¹ × 11¹ × 97¹
LCM(10656,10670) = 56849760