What is the Least Common Multiple of 33670 and 33688?

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 33670 and 33688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33670 and 33688, than apply into the LCM equation.

GCF(33670,33688) = 2
LCM(33670,33688) = ( 33670 × 33688) / 2
LCM(33670,33688) = 1134274960 / 2
LCM(33670,33688) = 567137480

Least Common Multiple (LCM) of 33670 and 33688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33670 and 33688. First we will calculate the prime factors of 33670 and 33688.

Prime Factorization of 33670

Prime Factorization of 33688

Now multiplying the highest exponent prime factors to calculate the LCM of 33670 and 33688.

LCM(33670,33688) = 2³ × 5¹ × 7¹ × 13¹ × 37¹ × 4211¹
LCM(33670,33688) = 567137480