What is the Least Common Multiple of 10214 and 10220?

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 10214 and 10220 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10214 and 10220, than apply into the LCM equation.

GCF(10214,10220) = 2
LCM(10214,10220) = ( 10214 × 10220) / 2
LCM(10214,10220) = 104387080 / 2
LCM(10214,10220) = 52193540

Least Common Multiple (LCM) of 10214 and 10220 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10214 and 10220. First we will calculate the prime factors of 10214 and 10220.

Prime Factorization of 10214

Prime Factorization of 10220

Now multiplying the highest exponent prime factors to calculate the LCM of 10214 and 10220.

LCM(10214,10220) = 2² × 5107¹ × 5¹ × 7¹ × 73¹
LCM(10214,10220) = 52193540