What is the Least Common Multiple of 21 and 32?
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 (LCM) of 21 and 32 is 672.
LCM(21,32) = 672
Least Common Multiple of 21 and 32 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21 and 32, than apply into the LCM equation.
GCF(21,32) = 1
LCM(21,32) = ( 21 × 32) / 1
LCM(21,32) = 672 / 1
LCM(21,32) = 672
Least Common Multiple (LCM) of 21 and 32 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 32. First we will calculate the prime factors of 21 and 32.
Prime Factorization of 21
Prime factors of 21 are 3, 7. Prime factorization of 21 in exponential form is:
21 = 31 × 71
Prime Factorization of 32
Prime factors of 32 are 2. Prime factorization of 32 in exponential form is:
32 = 25
Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 32.
LCM(21,32) = 31 × 71 × 25
LCM(21,32) = 672