What is the Least Common Multiple of 10414 and 10420?

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 10414 and 10420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10414 and 10420, than apply into the LCM equation.

GCF(10414,10420) = 2
LCM(10414,10420) = ( 10414 × 10420) / 2
LCM(10414,10420) = 108513880 / 2
LCM(10414,10420) = 54256940

Least Common Multiple (LCM) of 10414 and 10420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10414 and 10420. First we will calculate the prime factors of 10414 and 10420.

Prime Factorization of 10414

Prime Factorization of 10420

Now multiplying the highest exponent prime factors to calculate the LCM of 10414 and 10420.

LCM(10414,10420) = 2² × 41¹ × 127¹ × 5¹ × 521¹
LCM(10414,10420) = 54256940