What is the Least Common Multiple of 21 and 29?
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 29 is 609.
LCM(21,29) = 609
Least Common Multiple of 21 and 29 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 29, than apply into the LCM equation.
GCF(21,29) = 1
LCM(21,29) = ( 21 × 29) / 1
LCM(21,29) = 609 / 1
LCM(21,29) = 609
Least Common Multiple (LCM) of 21 and 29 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 29. First we will calculate the prime factors of 21 and 29.
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 29
Prime factors of 29 are 29. Prime factorization of 29 in exponential form is:
29 = 291
Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 29.
LCM(21,29) = 31 × 71 × 291
LCM(21,29) = 609