What is the Least Common Multiple of 10050 and 10070?

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 10050 and 10070 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10050 and 10070, than apply into the LCM equation.

GCF(10050,10070) = 10
LCM(10050,10070) = ( 10050 × 10070) / 10
LCM(10050,10070) = 101203500 / 10
LCM(10050,10070) = 10120350

Least Common Multiple (LCM) of 10050 and 10070 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10050 and 10070. First we will calculate the prime factors of 10050 and 10070.

Prime Factorization of 10050

Prime Factorization of 10070

Now multiplying the highest exponent prime factors to calculate the LCM of 10050 and 10070.

LCM(10050,10070) = 2¹ × 3¹ × 5² × 67¹ × 19¹ × 53¹
LCM(10050,10070) = 10120350