What is the Least Common Multiple of 30 and 37?
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 30 and 37 is 1110.
LCM(30,37) = 1110
Least Common Multiple of 30 and 37 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 37, than apply into the LCM equation.
GCF(30,37) = 1
LCM(30,37) = ( 30 × 37) / 1
LCM(30,37) = 1110 / 1
LCM(30,37) = 1110
Least Common Multiple (LCM) of 30 and 37 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 37. First we will calculate the prime factors of 30 and 37.
Prime Factorization of 30
Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:
30 = 21 × 31 × 51
Prime Factorization of 37
Prime factors of 37 are 37. Prime factorization of 37 in exponential form is:
37 = 371
Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 37.
LCM(30,37) = 21 × 31 × 51 × 371
LCM(30,37) = 1110