Least Common Multiple of 84 and 85

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 85 the smallest integer that is 7140 that is divisible by both numbers.

Least Common Multiple (LCM) of 84 and 85 is 7140.

LCM(84,85) = 7140

LCM of 84 and 85

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

LCM of:
and

Least Common Multiple of 84 and 85

LCM of 84 and 85 is 7140

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 85. First we will calculate the prime factors of 84 and 85.

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 85


5 85
17 17
1

Prime factors of 85 are 5,17. Prime factorization of 85 in exponential form is:

85 = 51×171

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 85.

LCM(84,85) = 22×31×51×71×171
LCM(84,85) = 7140

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 85

List of positive integer factors of 85 that divides 85 without a remainder.

1, 5, 17, 85

Least Common Multiple of 84 and 85 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 85, than apply into the LCM equation.

GCF(84,85) = 1
LCM(84,85) = ( 84 × 85) / 1
LCM(84,85) = 7140 / 1
LCM(84,85) = 7140

Properties of LCM 84 and 85

(i) The LCM of 85 and 84 is associative

LCM of 84 and 85 = LCM of 85 and 84

Related Least Common Multiples of 84

Related Least Common Multiples of 85

Frequently Asked Questions on LCM of 84 and 85

1. What is the LCM of 84 and 85?

Answer: LCM of 84 and 85 is 7140.

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 85?

Answer: Factors of 85 are 1, 5, 17, 85. There are 4 integers that are factors of 85. The greatest factor of 85 is 85.

4. How to Find the LCM of 84 and 85?

Answer:

Least Common Multiple of 84 and 85 = 7140

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 85

85 = 5 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 = 7140 = 2 x 2 x 3 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 84 and 85 is 7140.