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Least Common Multiple of 42 and 48

Free LCM Calculator determines the least common multiple (LCM) between 42 and 48 the smallest integer that is 336 that is divisible by both numbers.

Least Common Multiple (LCM) of 42 and 48 is 336.

LCM(42,48) = 336

LCM of 42 and 48

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

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


2 42
3 21
7 7
1

Prime factors of 42 are 2, 3,7. Prime factorization of 42 in exponential form is:

42 = 21×31×71

Prime Factorization of 48


2 48
2 24
2 12
2 6
3 3
1

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

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42

Factors of 48

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

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

Properties of LCM 42 and 48

(i) The LCM of 48 and 42 is associative

LCM of 42 and 48 = LCM of 48 and 42

Frequently Asked Questions on LCM of 42 and 48

1. What is the LCM of 42 and 48?

Answer: LCM of 42 and 48 is 336.

2. What are the Factors of 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

3. What are the Factors of 48?

Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.

4. How to Find the LCM of 42 and 48?

Answer:

Least Common Multiple of 42 and 48 = 336

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 48

48 = 2 x 2 x 2 x 2 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 336 = 2 x 2 x 2 x 2 x 3 x 7

Step 4: Therefore, the least common multiple of 42 and 48 is 336.