Least Common Multiple of 168 and 174

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 174 the smallest integer that is 4872 that is divisible by both numbers.

Least Common Multiple (LCM) of 168 and 174 is 4872.

LCM(168,174) = 4872

LCM of 168 and 174

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

LCM of:
and

Least Common Multiple of 168 and 174

LCM of 168 and 174 is 4872

Least common multiple can be found by multiplying the highest exponent prime factors of 168 and 174. First we will calculate the prime factors of 168 and 174.

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 174


2 174
3 87
29 29
1

Prime factors of 174 are 2, 3,29. Prime factorization of 174 in exponential form is:

174 = 21×31×291

Now multiplying the highest exponent prime factors to calculate the LCM of 168 and 174.

LCM(168,174) = 23×31×71×291
LCM(168,174) = 4872

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 174

List of positive integer factors of 174 that divides 174 without a remainder.

1, 2, 3, 6, 29, 58, 87, 174

Least Common Multiple of 168 and 174 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 174, than apply into the LCM equation.

GCF(168,174) = 6
LCM(168,174) = ( 168 × 174) / 6
LCM(168,174) = 29232 / 6
LCM(168,174) = 4872

Properties of LCM 168 and 174

(i) The LCM of 174 and 168 is associative

LCM of 168 and 174 = LCM of 174 and 168

Related Least Common Multiples of 168

Related Least Common Multiples of 174

Frequently Asked Questions on LCM of 168 and 174

1. What is the LCM of 168 and 174?

Answer: LCM of 168 and 174 is 4872.

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 174?

Answer: Factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174. There are 8 integers that are factors of 174. The greatest factor of 174 is 174.

4. How to Find the LCM of 168 and 174?

Answer:

Least Common Multiple of 168 and 174 = 4872

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 174

174 = 2 x 3 x 29

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

LCM = 4872 = 2 x 2 x 2 x 3 x 7 x 29

Step 4: Therefore, the least common multiple of 168 and 174 is 4872.