What is the Least Common Multiple of 5670 and 5688?

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 5670 and 5688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5670 and 5688, than apply into the LCM equation.

GCF(5670,5688) = 18
LCM(5670,5688) = ( 5670 × 5688) / 18
LCM(5670,5688) = 32250960 / 18
LCM(5670,5688) = 1791720

Least Common Multiple (LCM) of 5670 and 5688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5670 and 5688. First we will calculate the prime factors of 5670 and 5688.

Prime Factorization of 5670

Prime Factorization of 5688

Now multiplying the highest exponent prime factors to calculate the LCM of 5670 and 5688.

LCM(5670,5688) = 2³ × 3⁴ × 5¹ × 7¹ × 79¹
LCM(5670,5688) = 1791720