Question

Find the LCM and GCF for 30 and 48.

Answer 1

LCM is 240

GCF is 6

long explanation

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.

LCM(a,b) = ( a × b) / GCF(a,b)

We will now calculate the prime factors of 30 and 48, than find the greatest common factor (greatest common divisor (gcd) of the numbers by matching the biggest common factor of 30 and 48.

Step-1: Prime Factorization of 30

30 = 2^1 × 3^1 × 5^1

Step-2: Prime Factorization of 48

48 = 2^4 × 3^1

Step-3: Factors of 30

1, 2, 3, 5, 6, 10, 15

Step-4: Factors of 48

1, 2, 3, 4, 6, 8, 12, 16, 24

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30 and 48. The biggest common factor number is the GCF number.

So the greatest common factor 30 and 48 is 6.