Least Common Multiple of 168 and 175

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 175 the smallest integer that is 4200 that is divisible by both numbers.

Least Common Multiple (LCM) of 168 and 175 is 4200.

LCM(168,175) = 4200

LCM of 168 and 175

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

LCM of:
and

Least Common Multiple of 168 and 175

LCM of 168 and 175 is 4200

Least common multiple can be found by multiplying the highest exponent prime factors of 168 and 175. First we will calculate the prime factors of 168 and 175.

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 175


5 175
5 35
7 7
1

Prime factors of 175 are 5,7. Prime factorization of 175 in exponential form is:

175 = 52×71

Now multiplying the highest exponent prime factors to calculate the LCM of 168 and 175.

LCM(168,175) = 23×31×52×71
LCM(168,175) = 4200

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 175

List of positive integer factors of 175 that divides 175 without a remainder.

1, 5, 7, 25, 35, 175

Least Common Multiple of 168 and 175 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 175, than apply into the LCM equation.

GCF(168,175) = 7
LCM(168,175) = ( 168 × 175) / 7
LCM(168,175) = 29400 / 7
LCM(168,175) = 4200

Properties of LCM 168 and 175

(i) The LCM of 175 and 168 is associative

LCM of 168 and 175 = LCM of 175 and 168

Related Least Common Multiples of 168

Related Least Common Multiples of 175

Frequently Asked Questions on LCM of 168 and 175

1. What is the LCM of 168 and 175?

Answer: LCM of 168 and 175 is 4200.

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 175?

Answer: Factors of 175 are 1, 5, 7, 25, 35, 175. There are 6 integers that are factors of 175. The greatest factor of 175 is 175.

4. How to Find the LCM of 168 and 175?

Answer:

Least Common Multiple of 168 and 175 = 4200

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 175

175 = 5 x 5 x 7

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

LCM = 4200 = 2 x 2 x 2 x 3 x 5 x 5 x 7

Step 4: Therefore, the least common multiple of 168 and 175 is 4200.