What is the Least Common Multiple of 678 and 688?

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 678 and 688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 678 and 688, than apply into the LCM equation.

GCF(678,688) = 2
LCM(678,688) = ( 678 × 688) / 2
LCM(678,688) = 466464 / 2
LCM(678,688) = 233232

Least Common Multiple (LCM) of 678 and 688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 678 and 688. First we will calculate the prime factors of 678 and 688.

Prime Factorization of 678

Prime Factorization of 688

Now multiplying the highest exponent prime factors to calculate the LCM of 678 and 688.

LCM(678,688) = 2⁴ × 3¹ × 113¹ × 43¹
LCM(678,688) = 233232