Least Common Multiple of 369 and 374

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 369 and 374 the smallest integer that is 138006 that is divisible by both numbers.

Least Common Multiple (LCM) of 369 and 374 is 138006.

LCM(369,374) = 138006

LCM of 369 and 374

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

LCM of:
and

Least Common Multiple of 369 and 374

LCM of 369 and 374 is 138006

Least common multiple can be found by multiplying the highest exponent prime factors of 369 and 374. First we will calculate the prime factors of 369 and 374.

Prime Factorization of 369


3 369
3 123
41 41
1

Prime factors of 369 are 3,41. Prime factorization of 369 in exponential form is:

369 = 32×411

Prime Factorization of 374


2 374
11 187
17 17
1

Prime factors of 374 are 2, 11,17. Prime factorization of 374 in exponential form is:

374 = 21×111×171

Now multiplying the highest exponent prime factors to calculate the LCM of 369 and 374.

LCM(369,374) = 21×32×111×171×411
LCM(369,374) = 138006

Factors of 369

List of positive integer factors of 369 that divides 369 without a remainder.

1, 3, 9, 41, 123, 369

Factors of 374

List of positive integer factors of 374 that divides 374 without a remainder.

1, 2, 11, 17, 22, 34, 187, 374

Least Common Multiple of 369 and 374 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 369 and 374, than apply into the LCM equation.

GCF(369,374) = 1
LCM(369,374) = ( 369 × 374) / 1
LCM(369,374) = 138006 / 1
LCM(369,374) = 138006

Properties of LCM 369 and 374

(i) The LCM of 374 and 369 is associative

LCM of 369 and 374 = LCM of 374 and 369

Related Least Common Multiples of 369

Related Least Common Multiples of 374

Frequently Asked Questions on LCM of 369 and 374

1. What is the LCM of 369 and 374?

Answer: LCM of 369 and 374 is 138006.

2. What are the Factors of 369?

Answer: Factors of 369 are 1, 3, 9, 41, 123, 369. There are 6 integers that are factors of 369. The greatest factor of 369 is 369.

3. What are the Factors of 374?

Answer: Factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374. There are 8 integers that are factors of 374. The greatest factor of 374 is 374.

4. How to Find the LCM of 369 and 374?

Answer:

Least Common Multiple of 369 and 374 = 138006

Step 1: Find the prime factorization of 369

369 = 3 x 3 x 41

Step 2: Find the prime factorization of 374

374 = 2 x 11 x 17

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

LCM = 138006 = 2 x 3 x 3 x 11 x 17 x 41

Step 4: Therefore, the least common multiple of 369 and 374 is 138006.