Least Common Multiple of 31314 and 31320

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 31314 and 31320 the smallest integer that is 163459080 that is divisible by both numbers.

Least Common Multiple (LCM) of 31314 and 31320 is 163459080.

LCM(31314,31320) = 163459080

LCM of 31314 and 31320

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

LCM of:
and

Least Common Multiple of 31314 and 31320

LCM of 31314 and 31320 is 163459080

Least common multiple can be found by multiplying the highest exponent prime factors of 31314 and 31320. First we will calculate the prime factors of 31314 and 31320.

Prime Factorization of 31314


2 31314
3 15657
17 5219
307 307
1

Prime factors of 31314 are 2, 3, 17,307. Prime factorization of 31314 in exponential form is:

31314 = 21×31×171×3071

Prime Factorization of 31320


2 31320
2 15660
2 7830
3 3915
3 1305
3 435
5 145
29 29
1

Prime factors of 31320 are 2, 3, 5,29. Prime factorization of 31320 in exponential form is:

31320 = 23×33×51×291

Now multiplying the highest exponent prime factors to calculate the LCM of 31314 and 31320.

LCM(31314,31320) = 23×33×51×171×291×3071
LCM(31314,31320) = 163459080

Factors of 31314

List of positive integer factors of 31314 that divides 31314 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657, 31314

Factors of 31320

List of positive integer factors of 31320 that divides 31320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 29, 30, 36, 40, 45, 54, 58, 60, 72, 87, 90, 108, 116, 120, 135, 145, 174, 180, 216, 232, 261, 270, 290, 348, 360, 435, 522, 540, 580, 696, 783, 870, 1044, 1080, 1160, 1305, 1566, 1740, 2088, 2610, 3132, 3480, 3915, 5220, 6264, 7830, 10440, 15660, 31320

Least Common Multiple of 31314 and 31320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31314 and 31320, than apply into the LCM equation.

GCF(31314,31320) = 6
LCM(31314,31320) = ( 31314 × 31320) / 6
LCM(31314,31320) = 980754480 / 6
LCM(31314,31320) = 163459080

Properties of LCM 31314 and 31320

(i) The LCM of 31320 and 31314 is associative

LCM of 31314 and 31320 = LCM of 31320 and 31314

Related Least Common Multiples of 31314

Related Least Common Multiples of 31320

Frequently Asked Questions on LCM of 31314 and 31320

1. What is the LCM of 31314 and 31320?

Answer: LCM of 31314 and 31320 is 163459080.

2. What are the Factors of 31314?

Answer: Factors of 31314 are 1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657, 31314. There are 16 integers that are factors of 31314. The greatest factor of 31314 is 31314.

3. What are the Factors of 31320?

Answer: Factors of 31320 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 29, 30, 36, 40, 45, 54, 58, 60, 72, 87, 90, 108, 116, 120, 135, 145, 174, 180, 216, 232, 261, 270, 290, 348, 360, 435, 522, 540, 580, 696, 783, 870, 1044, 1080, 1160, 1305, 1566, 1740, 2088, 2610, 3132, 3480, 3915, 5220, 6264, 7830, 10440, 15660, 31320. There are 64 integers that are factors of 31320. The greatest factor of 31320 is 31320.

4. How to Find the LCM of 31314 and 31320?

Answer:

Least Common Multiple of 31314 and 31320 = 163459080

Step 1: Find the prime factorization of 31314

31314 = 2 x 3 x 17 x 307

Step 2: Find the prime factorization of 31320

31320 = 2 x 2 x 2 x 3 x 3 x 3 x 5 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 = 163459080 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 17 x 29 x 307

Step 4: Therefore, the least common multiple of 31314 and 31320 is 163459080.