What is the Least Common Multiple of 21996 and 22009?

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 21996 and 22009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21996 and 22009, than apply into the LCM equation.

GCF(21996,22009) = 13
LCM(21996,22009) = ( 21996 × 22009) / 13
LCM(21996,22009) = 484109964 / 13
LCM(21996,22009) = 37239228

Least Common Multiple (LCM) of 21996 and 22009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21996 and 22009. First we will calculate the prime factors of 21996 and 22009.

Prime Factorization of 21996

Prime Factorization of 22009

Now multiplying the highest exponent prime factors to calculate the LCM of 21996 and 22009.

LCM(21996,22009) = 2² × 3² × 13¹ × 47¹ × 1693¹
LCM(21996,22009) = 37239228