Least Common Multiple of 48 and 67

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 67 the smallest integer that is 3216 that is divisible by both numbers.

Least Common Multiple (LCM) of 48 and 67 is 3216.

LCM(48,67) = 3216

LCM of 48 and 67

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

LCM of:
and

Least Common Multiple of 48 and 67

LCM of 48 and 67 is 3216

Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 67. First we will calculate the prime factors of 48 and 67.

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 67


67 67
1

Prime factors of 67 are 67. Prime factorization of 67 in exponential form is:

67 = 671

Now multiplying the highest exponent prime factors to calculate the LCM of 48 and 67.

LCM(48,67) = 24×31×671
LCM(48,67) = 3216

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 67

List of positive integer factors of 67 that divides 67 without a remainder.

1, 67

Least Common Multiple of 48 and 67 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 67, than apply into the LCM equation.

GCF(48,67) = 1
LCM(48,67) = ( 48 × 67) / 1
LCM(48,67) = 3216 / 1
LCM(48,67) = 3216

Properties of LCM 48 and 67

(i) The LCM of 67 and 48 is associative

LCM of 48 and 67 = LCM of 67 and 48

Related Least Common Multiples of 48

Related Least Common Multiples of 67

Frequently Asked Questions on LCM of 48 and 67

1. What is the LCM of 48 and 67?

Answer: LCM of 48 and 67 is 3216.

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 67?

Answer: Factors of 67 are 1, 67. There are 2 integers that are factors of 67. The greatest factor of 67 is 67.

4. How to Find the LCM of 48 and 67?

Answer:

Least Common Multiple of 48 and 67 = 3216

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 67

67 = 67

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

LCM = 3216 = 2 x 2 x 2 x 2 x 3 x 67

Step 4: Therefore, the least common multiple of 48 and 67 is 3216.