Least Common Multiple of 174 and 180

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 174 and 180 the smallest integer that is 5220 that is divisible by both numbers.

Least Common Multiple (LCM) of 174 and 180 is 5220.

LCM(174,180) = 5220

LCM of 174 and 180

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

LCM of:
and

Least Common Multiple of 174 and 180

LCM of 174 and 180 is 5220

Least common multiple can be found by multiplying the highest exponent prime factors of 174 and 180. First we will calculate the prime factors of 174 and 180.

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

Prime Factorization of 180


2 180
2 90
3 45
3 15
5 5
1

Prime factors of 180 are 2, 3,5. Prime factorization of 180 in exponential form is:

180 = 22×32×51

Now multiplying the highest exponent prime factors to calculate the LCM of 174 and 180.

LCM(174,180) = 22×32×51×291
LCM(174,180) = 5220

Factors of 174

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

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

Factors of 180

List of positive integer factors of 180 that divides 180 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

Least Common Multiple of 174 and 180 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 174 and 180, than apply into the LCM equation.

GCF(174,180) = 6
LCM(174,180) = ( 174 × 180) / 6
LCM(174,180) = 31320 / 6
LCM(174,180) = 5220

Properties of LCM 174 and 180

(i) The LCM of 180 and 174 is associative

LCM of 174 and 180 = LCM of 180 and 174

Related Least Common Multiples of 174

Related Least Common Multiples of 180

Frequently Asked Questions on LCM of 174 and 180

1. What is the LCM of 174 and 180?

Answer: LCM of 174 and 180 is 5220.

2. 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.

3. What are the Factors of 180?

Answer: Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. There are 18 integers that are factors of 180. The greatest factor of 180 is 180.

4. How to Find the LCM of 174 and 180?

Answer:

Least Common Multiple of 174 and 180 = 5220

Step 1: Find the prime factorization of 174

174 = 2 x 3 x 29

Step 2: Find the prime factorization of 180

180 = 2 x 2 x 3 x 3 x 5

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

LCM = 5220 = 2 x 2 x 3 x 3 x 5 x 29

Step 4: Therefore, the least common multiple of 174 and 180 is 5220.