Least Common Multiple of 84 and 91

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 91 the smallest integer that is 1092 that is divisible by both numbers.

Least Common Multiple (LCM) of 84 and 91 is 1092.

LCM(84,91) = 1092

LCM of 84 and 91

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

LCM of:
and

Least Common Multiple of 84 and 91

LCM of 84 and 91 is 1092

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 91. First we will calculate the prime factors of 84 and 91.

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 91


7 91
13 13
1

Prime factors of 91 are 7,13. Prime factorization of 91 in exponential form is:

91 = 71×131

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 91.

LCM(84,91) = 22×31×71×131
LCM(84,91) = 1092

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 91

List of positive integer factors of 91 that divides 91 without a remainder.

1, 7, 13, 91

Least Common Multiple of 84 and 91 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 91, than apply into the LCM equation.

GCF(84,91) = 7
LCM(84,91) = ( 84 × 91) / 7
LCM(84,91) = 7644 / 7
LCM(84,91) = 1092

Properties of LCM 84 and 91

(i) The LCM of 91 and 84 is associative

LCM of 84 and 91 = LCM of 91 and 84

Related Least Common Multiples of 84

Related Least Common Multiples of 91

Frequently Asked Questions on LCM of 84 and 91

1. What is the LCM of 84 and 91?

Answer: LCM of 84 and 91 is 1092.

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 91?

Answer: Factors of 91 are 1, 7, 13, 91. There are 4 integers that are factors of 91. The greatest factor of 91 is 91.

4. How to Find the LCM of 84 and 91?

Answer:

Least Common Multiple of 84 and 91 = 1092

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 91

91 = 7 x 13

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

LCM = 1092 = 2 x 2 x 3 x 7 x 13

Step 4: Therefore, the least common multiple of 84 and 91 is 1092.