Least Common Multiple of 84 and 101

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 84 and 101 the smallest integer that is 8484 that is divisible by both numbers.

Least Common Multiple (LCM) of 84 and 101 is 8484.

LCM(84,101) = 8484

LCM of 84 and 101

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

LCM of:
and

Least Common Multiple of 84 and 101

LCM of 84 and 101 is 8484

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 101. First we will calculate the prime factors of 84 and 101.

Prime Factorization of 84


2 84
2 42
3 21
7 7
1

Prime factors of 84 are 2, 3,7. Prime factorization of 84 in exponential form is:

84 = 22×31×71

Prime Factorization of 101


101 101
1

Prime factors of 101 are 101. Prime factorization of 101 in exponential form is:

101 = 1011

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 101.

LCM(84,101) = 22×31×71×1011
LCM(84,101) = 8484

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Factors of 101

List of positive integer factors of 101 that divides 101 without a remainder.

1, 101

Least Common Multiple of 84 and 101 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84 and 101, than apply into the LCM equation.

GCF(84,101) = 1
LCM(84,101) = ( 84 × 101) / 1
LCM(84,101) = 8484 / 1
LCM(84,101) = 8484

Properties of LCM 84 and 101

(i) The LCM of 101 and 84 is associative

LCM of 84 and 101 = LCM of 101 and 84

Related Least Common Multiples of 84

Related Least Common Multiples of 101

Frequently Asked Questions on LCM of 84 and 101

1. What is the LCM of 84 and 101?

Answer: LCM of 84 and 101 is 8484.

2. What are the Factors of 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

3. What are the Factors of 101?

Answer: Factors of 101 are 1, 101. There are 2 integers that are factors of 101. The greatest factor of 101 is 101.

4. How to Find the LCM of 84 and 101?

Answer:

Least Common Multiple of 84 and 101 = 8484

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 101

101 = 101

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

LCM = 8484 = 2 x 2 x 3 x 7 x 101

Step 4: Therefore, the least common multiple of 84 and 101 is 8484.