What is the Least Common Multiple of 5678 and 5689?

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 5678 and 5689 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5678 and 5689, than apply into the LCM equation.

GCF(5678,5689) = 1
LCM(5678,5689) = ( 5678 × 5689) / 1
LCM(5678,5689) = 32302142 / 1
LCM(5678,5689) = 32302142

Least Common Multiple (LCM) of 5678 and 5689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5678 and 5689. First we will calculate the prime factors of 5678 and 5689.

Prime Factorization of 5678

Prime Factorization of 5689

Now multiplying the highest exponent prime factors to calculate the LCM of 5678 and 5689.

LCM(5678,5689) = 2¹ × 17¹ × 167¹ × 5689¹
LCM(5678,5689) = 32302142