Least Common Multiple of 84 and 93

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 93 the smallest integer that is 2604 that is divisible by both numbers.

Least Common Multiple (LCM) of 84 and 93 is 2604.

LCM(84,93) = 2604

LCM of 84 and 93

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

LCM of:
and

Least Common Multiple of 84 and 93

LCM of 84 and 93 is 2604

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 93. First we will calculate the prime factors of 84 and 93.

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 93


3 93
31 31
1

Prime factors of 93 are 3,31. Prime factorization of 93 in exponential form is:

93 = 31×311

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 93.

LCM(84,93) = 22×31×71×311
LCM(84,93) = 2604

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 93

List of positive integer factors of 93 that divides 93 without a remainder.

1, 3, 31, 93

Least Common Multiple of 84 and 93 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 93, than apply into the LCM equation.

GCF(84,93) = 3
LCM(84,93) = ( 84 × 93) / 3
LCM(84,93) = 7812 / 3
LCM(84,93) = 2604

Properties of LCM 84 and 93

(i) The LCM of 93 and 84 is associative

LCM of 84 and 93 = LCM of 93 and 84

Related Least Common Multiples of 84

Related Least Common Multiples of 93

Frequently Asked Questions on LCM of 84 and 93

1. What is the LCM of 84 and 93?

Answer: LCM of 84 and 93 is 2604.

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 93?

Answer: Factors of 93 are 1, 3, 31, 93. There are 4 integers that are factors of 93. The greatest factor of 93 is 93.

4. How to Find the LCM of 84 and 93?

Answer:

Least Common Multiple of 84 and 93 = 2604

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 93

93 = 3 x 31

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

LCM = 2604 = 2 x 2 x 3 x 7 x 31

Step 4: Therefore, the least common multiple of 84 and 93 is 2604.