Least Common Multiple of 336 and 342

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 336 and 342 the smallest integer that is 19152 that is divisible by both numbers.

Least Common Multiple (LCM) of 336 and 342 is 19152.

LCM(336,342) = 19152

LCM of 336 and 342

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

LCM of:
and

Least Common Multiple of 336 and 342

LCM of 336 and 342 is 19152

Least common multiple can be found by multiplying the highest exponent prime factors of 336 and 342. First we will calculate the prime factors of 336 and 342.

Prime Factorization of 336


2 336
2 168
2 84
2 42
3 21
7 7
1

Prime factors of 336 are 2, 3,7. Prime factorization of 336 in exponential form is:

336 = 24×31×71

Prime Factorization of 342


2 342
3 171
3 57
19 19
1

Prime factors of 342 are 2, 3,19. Prime factorization of 342 in exponential form is:

342 = 21×32×191

Now multiplying the highest exponent prime factors to calculate the LCM of 336 and 342.

LCM(336,342) = 24×32×71×191
LCM(336,342) = 19152

Factors of 336

List of positive integer factors of 336 that divides 336 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336

Factors of 342

List of positive integer factors of 342 that divides 342 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342

Least Common Multiple of 336 and 342 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 336 and 342, than apply into the LCM equation.

GCF(336,342) = 6
LCM(336,342) = ( 336 × 342) / 6
LCM(336,342) = 114912 / 6
LCM(336,342) = 19152

Properties of LCM 336 and 342

(i) The LCM of 342 and 336 is associative

LCM of 336 and 342 = LCM of 342 and 336

Related Least Common Multiples of 336

Related Least Common Multiples of 342

Frequently Asked Questions on LCM of 336 and 342

1. What is the LCM of 336 and 342?

Answer: LCM of 336 and 342 is 19152.

2. What are the Factors of 336?

Answer: Factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336. There are 20 integers that are factors of 336. The greatest factor of 336 is 336.

3. What are the Factors of 342?

Answer: Factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342. There are 12 integers that are factors of 342. The greatest factor of 342 is 342.

4. How to Find the LCM of 336 and 342?

Answer:

Least Common Multiple of 336 and 342 = 19152

Step 1: Find the prime factorization of 336

336 = 2 x 2 x 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 342

342 = 2 x 3 x 3 x 19

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

LCM = 19152 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 19

Step 4: Therefore, the least common multiple of 336 and 342 is 19152.