What is the Least Common Multiple of 48 and 170?
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 48 and 170 is 4080.
LCM(48,170) = 4080
Least Common Multiple of 48 and 170 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48 and 170, than apply into the LCM equation.
GCF(48,170) = 2
LCM(48,170) = ( 48 × 170) / 2
LCM(48,170) = 8160 / 2
LCM(48,170) = 4080
Least Common Multiple (LCM) of 48 and 170 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 170. First we will calculate the prime factors of 48 and 170.
Prime Factorization of 48
Prime factors of 48 are 2, 3. Prime factorization of 48 in exponential form is:
48 = 24 × 31
Prime Factorization of 170
Prime factors of 170 are 2, 5, 17. Prime factorization of 170 in exponential form is:
170 = 21 × 51 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 48 and 170.
LCM(48,170) = 24 × 31 × 51 × 171
LCM(48,170) = 4080
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