Least Common Multiple of 31410 and 31414

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 31410 and 31414 the smallest integer that is 493356870 that is divisible by both numbers.

Least Common Multiple (LCM) of 31410 and 31414 is 493356870.

LCM(31410,31414) = 493356870

LCM of 31410 and 31414

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

LCM of:
and

Least Common Multiple of 31410 and 31414

LCM of 31410 and 31414 is 493356870

Least common multiple can be found by multiplying the highest exponent prime factors of 31410 and 31414. First we will calculate the prime factors of 31410 and 31414.

Prime Factorization of 31410


2 31410
3 15705
3 5235
5 1745
349 349
1

Prime factors of 31410 are 2, 3, 5,349. Prime factorization of 31410 in exponential form is:

31410 = 21×32×51×3491

Prime Factorization of 31414


2 31414
113 15707
139 139
1

Prime factors of 31414 are 2, 113,139. Prime factorization of 31414 in exponential form is:

31414 = 21×1131×1391

Now multiplying the highest exponent prime factors to calculate the LCM of 31410 and 31414.

LCM(31410,31414) = 21×32×51×1131×1391×3491
LCM(31410,31414) = 493356870

Factors of 31410

List of positive integer factors of 31410 that divides 31410 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 349, 698, 1047, 1745, 2094, 3141, 3490, 5235, 6282, 10470, 15705, 31410

Factors of 31414

List of positive integer factors of 31414 that divides 31414 without a remainder.

1, 2, 113, 139, 226, 278, 15707, 31414

Least Common Multiple of 31410 and 31414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31410 and 31414, than apply into the LCM equation.

GCF(31410,31414) = 2
LCM(31410,31414) = ( 31410 × 31414) / 2
LCM(31410,31414) = 986713740 / 2
LCM(31410,31414) = 493356870

Properties of LCM 31410 and 31414

(i) The LCM of 31414 and 31410 is associative

LCM of 31410 and 31414 = LCM of 31414 and 31410

Related Least Common Multiples of 31410

Related Least Common Multiples of 31414

Frequently Asked Questions on LCM of 31410 and 31414

1. What is the LCM of 31410 and 31414?

Answer: LCM of 31410 and 31414 is 493356870.

2. What are the Factors of 31410?

Answer: Factors of 31410 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 349, 698, 1047, 1745, 2094, 3141, 3490, 5235, 6282, 10470, 15705, 31410. There are 24 integers that are factors of 31410. The greatest factor of 31410 is 31410.

3. What are the Factors of 31414?

Answer: Factors of 31414 are 1, 2, 113, 139, 226, 278, 15707, 31414. There are 8 integers that are factors of 31414. The greatest factor of 31414 is 31414.

4. How to Find the LCM of 31410 and 31414?

Answer:

Least Common Multiple of 31410 and 31414 = 493356870

Step 1: Find the prime factorization of 31410

31410 = 2 x 3 x 3 x 5 x 349

Step 2: Find the prime factorization of 31414

31414 = 2 x 113 x 139

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

LCM = 493356870 = 2 x 3 x 3 x 5 x 113 x 139 x 349

Step 4: Therefore, the least common multiple of 31410 and 31414 is 493356870.