Least Common Multiple of 5736 and 5742

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 5736 and 5742 the smallest integer that is 5489352 that is divisible by both numbers.

Least Common Multiple (LCM) of 5736 and 5742 is 5489352.

LCM(5736,5742) = 5489352

LCM of 5736 and 5742

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

LCM of:
and

Least Common Multiple of 5736 and 5742

LCM of 5736 and 5742 is 5489352

Least common multiple can be found by multiplying the highest exponent prime factors of 5736 and 5742. First we will calculate the prime factors of 5736 and 5742.

Prime Factorization of 5736


2 5736
2 2868
2 1434
3 717
239 239
1

Prime factors of 5736 are 2, 3,239. Prime factorization of 5736 in exponential form is:

5736 = 23×31×2391

Prime Factorization of 5742


2 5742
3 2871
3 957
11 319
29 29
1

Prime factors of 5742 are 2, 3, 11,29. Prime factorization of 5742 in exponential form is:

5742 = 21×32×111×291

Now multiplying the highest exponent prime factors to calculate the LCM of 5736 and 5742.

LCM(5736,5742) = 23×32×111×291×2391
LCM(5736,5742) = 5489352

Factors of 5736

List of positive integer factors of 5736 that divides 5736 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 239, 478, 717, 956, 1434, 1912, 2868, 5736

Factors of 5742

List of positive integer factors of 5742 that divides 5742 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 29, 33, 58, 66, 87, 99, 174, 198, 261, 319, 522, 638, 957, 1914, 2871, 5742

Least Common Multiple of 5736 and 5742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5736 and 5742, than apply into the LCM equation.

GCF(5736,5742) = 6
LCM(5736,5742) = ( 5736 × 5742) / 6
LCM(5736,5742) = 32936112 / 6
LCM(5736,5742) = 5489352

Properties of LCM 5736 and 5742

(i) The LCM of 5742 and 5736 is associative

LCM of 5736 and 5742 = LCM of 5742 and 5736

Related Least Common Multiples of 5736

Related Least Common Multiples of 5742

Frequently Asked Questions on LCM of 5736 and 5742

1. What is the LCM of 5736 and 5742?

Answer: LCM of 5736 and 5742 is 5489352.

2. What are the Factors of 5736?

Answer: Factors of 5736 are 1, 2, 3, 4, 6, 8, 12, 24, 239, 478, 717, 956, 1434, 1912, 2868, 5736. There are 16 integers that are factors of 5736. The greatest factor of 5736 is 5736.

3. What are the Factors of 5742?

Answer: Factors of 5742 are 1, 2, 3, 6, 9, 11, 18, 22, 29, 33, 58, 66, 87, 99, 174, 198, 261, 319, 522, 638, 957, 1914, 2871, 5742. There are 24 integers that are factors of 5742. The greatest factor of 5742 is 5742.

4. How to Find the LCM of 5736 and 5742?

Answer:

Least Common Multiple of 5736 and 5742 = 5489352

Step 1: Find the prime factorization of 5736

5736 = 2 x 2 x 2 x 3 x 239

Step 2: Find the prime factorization of 5742

5742 = 2 x 3 x 3 x 11 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 = 5489352 = 2 x 2 x 2 x 3 x 3 x 11 x 29 x 239

Step 4: Therefore, the least common multiple of 5736 and 5742 is 5489352.