What is the Least Common Multiple of 5670 and 5678?

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 5678 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 5678, than apply into the LCM equation.

GCF(5670,5678) = 2
LCM(5670,5678) = ( 5670 × 5678) / 2
LCM(5670,5678) = 32194260 / 2
LCM(5670,5678) = 16097130

Least Common Multiple (LCM) of 5670 and 5678 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5670 and 5678. First we will calculate the prime factors of 5670 and 5678.

Prime Factorization of 5670

Prime Factorization of 5678

Now multiplying the highest exponent prime factors to calculate the LCM of 5670 and 5678.

LCM(5670,5678) = 2¹ × 3⁴ × 5¹ × 7¹ × 17¹ × 167¹
LCM(5670,5678) = 16097130