What is the Least Common Multiple of 342 and 350?
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 342 and 350 is 59850.
LCM(342,350) = 59850
Least Common Multiple of 342 and 350 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 342 and 350, than apply into the LCM equation.
GCF(342,350) = 2
LCM(342,350) = ( 342 × 350) / 2
LCM(342,350) = 119700 / 2
LCM(342,350) = 59850
Least Common Multiple (LCM) of 342 and 350 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 342 and 350. First we will calculate the prime factors of 342 and 350.
Prime Factorization of 342
Prime factors of 342 are 2, 3, 19. Prime factorization of 342 in exponential form is:
342 = 21 × 32 × 191
Prime Factorization of 350
Prime factors of 350 are 2, 5, 7. Prime factorization of 350 in exponential form is:
350 = 21 × 52 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 342 and 350.
LCM(342,350) = 21 × 32 × 191 × 52 × 71
LCM(342,350) = 59850
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