What is the Least Common Multiple of 30 and 35?
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 35 is 210.
LCM(30,35) = 210
Least Common Multiple of 30 and 35 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 35, than apply into the LCM equation.
GCF(30,35) = 5
LCM(30,35) = ( 30 × 35) / 5
LCM(30,35) = 1050 / 5
LCM(30,35) = 210
Least Common Multiple (LCM) of 30 and 35 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 35. First we will calculate the prime factors of 30 and 35.
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 35
Prime factors of 35 are 5, 7. Prime factorization of 35 in exponential form is:
35 = 51 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 35.
LCM(30,35) = 21 × 31 × 51 × 71
LCM(30,35) = 210