Least Common Multiple of 168 and 172

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 168 and 172 the smallest integer that is 7224 that is divisible by both numbers.

Least Common Multiple (LCM) of 168 and 172 is 7224.

LCM(168,172) = 7224

LCM of 168 and 172

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

LCM of:
and

Least Common Multiple of 168 and 172

LCM of 168 and 172 is 7224

Least common multiple can be found by multiplying the highest exponent prime factors of 168 and 172. First we will calculate the prime factors of 168 and 172.

Prime Factorization of 168


2 168
2 84
2 42
3 21
7 7
1

Prime factors of 168 are 2, 3,7. Prime factorization of 168 in exponential form is:

168 = 23×31×71

Prime Factorization of 172


2 172
2 86
43 43
1

Prime factors of 172 are 2,43. Prime factorization of 172 in exponential form is:

172 = 22×431

Now multiplying the highest exponent prime factors to calculate the LCM of 168 and 172.

LCM(168,172) = 23×31×71×431
LCM(168,172) = 7224

Factors of 168

List of positive integer factors of 168 that divides 168 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

Factors of 172

List of positive integer factors of 172 that divides 172 without a remainder.

1, 2, 4, 43, 86, 172

Least Common Multiple of 168 and 172 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 168 and 172, than apply into the LCM equation.

GCF(168,172) = 4
LCM(168,172) = ( 168 × 172) / 4
LCM(168,172) = 28896 / 4
LCM(168,172) = 7224

Properties of LCM 168 and 172

(i) The LCM of 172 and 168 is associative

LCM of 168 and 172 = LCM of 172 and 168

Related Least Common Multiples of 168

Related Least Common Multiples of 172

Frequently Asked Questions on LCM of 168 and 172

1. What is the LCM of 168 and 172?

Answer: LCM of 168 and 172 is 7224.

2. What are the Factors of 168?

Answer: Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. There are 16 integers that are factors of 168. The greatest factor of 168 is 168.

3. What are the Factors of 172?

Answer: Factors of 172 are 1, 2, 4, 43, 86, 172. There are 6 integers that are factors of 172. The greatest factor of 172 is 172.

4. How to Find the LCM of 168 and 172?

Answer:

Least Common Multiple of 168 and 172 = 7224

Step 1: Find the prime factorization of 168

168 = 2 x 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 172

172 = 2 x 2 x 43

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

LCM = 7224 = 2 x 2 x 2 x 3 x 7 x 43

Step 4: Therefore, the least common multiple of 168 and 172 is 7224.