What is the Least Common Multiple of 42 and 48?
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 42 and 48 is 336.
LCM(42,48) = 336
Least Common Multiple of 42 and 48 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42 and 48, than apply into the LCM equation.
GCF(42,48) = 6
LCM(42,48) = ( 42 × 48) / 6
LCM(42,48) = 2016 / 6
LCM(42,48) = 336
Least Common Multiple (LCM) of 42 and 48 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 48. First we will calculate the prime factors of 42 and 48.
Prime Factorization of 42
Prime factors of 42 are 2, 3, 7. Prime factorization of 42 in exponential form is:
42 = 21 × 31 × 71
Prime Factorization of 48
Prime factors of 48 are 2, 3. Prime factorization of 48 in exponential form is:
48 = 24 × 31
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 48.
LCM(42,48) = 24 × 31 × 71
LCM(42,48) = 336