Least Common Multiple of 48 and 68

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 48 and 68 the smallest integer that is 816 that is divisible by both numbers.

Least Common Multiple (LCM) of 48 and 68 is 816.

LCM(48,68) = 816

LCM of 48 and 68

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

LCM of:
and

Least Common Multiple of 48 and 68

LCM of 48 and 68 is 816

Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 68. First we will calculate the prime factors of 48 and 68.

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

Prime Factorization of 68


2 68
2 34
17 17
1

Prime factors of 68 are 2,17. Prime factorization of 68 in exponential form is:

68 = 22×171

Now multiplying the highest exponent prime factors to calculate the LCM of 48 and 68.

LCM(48,68) = 24×31×171
LCM(48,68) = 816

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

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1, 2, 4, 17, 34, 68

Least Common Multiple of 48 and 68 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 68, than apply into the LCM equation.

GCF(48,68) = 4
LCM(48,68) = ( 48 × 68) / 4
LCM(48,68) = 3264 / 4
LCM(48,68) = 816

Properties of LCM 48 and 68

(i) The LCM of 68 and 48 is associative

LCM of 48 and 68 = LCM of 68 and 48

Related Least Common Multiples of 48

Related Least Common Multiples of 68

Frequently Asked Questions on LCM of 48 and 68

1. What is the LCM of 48 and 68?

Answer: LCM of 48 and 68 is 816.

2. 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.

3. What are the Factors of 68?

Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.

4. How to Find the LCM of 48 and 68?

Answer:

Least Common Multiple of 48 and 68 = 816

Step 1: Find the prime factorization of 48

48 = 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 68

68 = 2 x 2 x 17

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

LCM = 816 = 2 x 2 x 2 x 2 x 3 x 17

Step 4: Therefore, the least common multiple of 48 and 68 is 816.