Least Common Multiple of 31416 and 31424

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 31416 and 31424 the smallest integer that is 123402048 that is divisible by both numbers.

Least Common Multiple (LCM) of 31416 and 31424 is 123402048.

LCM(31416,31424) = 123402048

LCM of 31416 and 31424

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

LCM of:
and

Least Common Multiple of 31416 and 31424

LCM of 31416 and 31424 is 123402048

Least common multiple can be found by multiplying the highest exponent prime factors of 31416 and 31424. First we will calculate the prime factors of 31416 and 31424.

Prime Factorization of 31416


2 31416
2 15708
2 7854
3 3927
7 1309
11 187
17 17
1

Prime factors of 31416 are 2, 3, 7, 11,17. Prime factorization of 31416 in exponential form is:

31416 = 23×31×71×111×171

Prime Factorization of 31424


2 31424
2 15712
2 7856
2 3928
2 1964
2 982
491 491
1

Prime factors of 31424 are 2,491. Prime factorization of 31424 in exponential form is:

31424 = 26×4911

Now multiplying the highest exponent prime factors to calculate the LCM of 31416 and 31424.

LCM(31416,31424) = 26×31×71×111×171×4911
LCM(31416,31424) = 123402048

Factors of 31416

List of positive integer factors of 31416 that divides 31416 without a remainder.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 17, 21, 22, 24, 28, 33, 34, 42, 44, 51, 56, 66, 68, 77, 84, 88, 102, 119, 132, 136, 154, 168, 187, 204, 231, 238, 264, 308, 357, 374, 408, 462, 476, 561, 616, 714, 748, 924, 952, 1122, 1309, 1428, 1496, 1848, 2244, 2618, 2856, 3927, 4488, 5236, 7854, 10472, 15708, 31416

Factors of 31424

List of positive integer factors of 31424 that divides 31424 without a remainder.

1, 2, 4, 8, 16, 32, 64, 491, 982, 1964, 3928, 7856, 15712, 31424

Least Common Multiple of 31416 and 31424 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31416 and 31424, than apply into the LCM equation.

GCF(31416,31424) = 8
LCM(31416,31424) = ( 31416 × 31424) / 8
LCM(31416,31424) = 987216384 / 8
LCM(31416,31424) = 123402048

Properties of LCM 31416 and 31424

(i) The LCM of 31424 and 31416 is associative

LCM of 31416 and 31424 = LCM of 31424 and 31416

Related Least Common Multiples of 31416

Related Least Common Multiples of 31424

Frequently Asked Questions on LCM of 31416 and 31424

1. What is the LCM of 31416 and 31424?

Answer: LCM of 31416 and 31424 is 123402048.

2. What are the Factors of 31416?

Answer: Factors of 31416 are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 17, 21, 22, 24, 28, 33, 34, 42, 44, 51, 56, 66, 68, 77, 84, 88, 102, 119, 132, 136, 154, 168, 187, 204, 231, 238, 264, 308, 357, 374, 408, 462, 476, 561, 616, 714, 748, 924, 952, 1122, 1309, 1428, 1496, 1848, 2244, 2618, 2856, 3927, 4488, 5236, 7854, 10472, 15708, 31416. There are 64 integers that are factors of 31416. The greatest factor of 31416 is 31416.

3. What are the Factors of 31424?

Answer: Factors of 31424 are 1, 2, 4, 8, 16, 32, 64, 491, 982, 1964, 3928, 7856, 15712, 31424. There are 14 integers that are factors of 31424. The greatest factor of 31424 is 31424.

4. How to Find the LCM of 31416 and 31424?

Answer:

Least Common Multiple of 31416 and 31424 = 123402048

Step 1: Find the prime factorization of 31416

31416 = 2 x 2 x 2 x 3 x 7 x 11 x 17

Step 2: Find the prime factorization of 31424

31424 = 2 x 2 x 2 x 2 x 2 x 2 x 491

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

LCM = 123402048 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 11 x 17 x 491

Step 4: Therefore, the least common multiple of 31416 and 31424 is 123402048.