Least Common Multiple of 10312 and 10320

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10312 and 10320 the smallest integer that is 13302480 that is divisible by both numbers.

Least Common Multiple (LCM) of 10312 and 10320 is 13302480.

LCM(10312,10320) = 13302480

LCM of 10312 and 10320

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

LCM of:
and

Least Common Multiple of 10312 and 10320

LCM of 10312 and 10320 is 13302480

Least common multiple can be found by multiplying the highest exponent prime factors of 10312 and 10320. First we will calculate the prime factors of 10312 and 10320.

Prime Factorization of 10312


2 10312
2 5156
2 2578
1289 1289
1

Prime factors of 10312 are 2,1289. Prime factorization of 10312 in exponential form is:

10312 = 23×12891

Prime Factorization of 10320


2 10320
2 5160
2 2580
2 1290
3 645
5 215
43 43
1

Prime factors of 10320 are 2, 3, 5,43. Prime factorization of 10320 in exponential form is:

10320 = 24×31×51×431

Now multiplying the highest exponent prime factors to calculate the LCM of 10312 and 10320.

LCM(10312,10320) = 24×31×51×431×12891
LCM(10312,10320) = 13302480

Factors of 10312

List of positive integer factors of 10312 that divides 10312 without a remainder.

1, 2, 4, 8, 1289, 2578, 5156, 10312

Factors of 10320

List of positive integer factors of 10320 that divides 10320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 43, 48, 60, 80, 86, 120, 129, 172, 215, 240, 258, 344, 430, 516, 645, 688, 860, 1032, 1290, 1720, 2064, 2580, 3440, 5160, 10320

Least Common Multiple of 10312 and 10320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10312 and 10320, than apply into the LCM equation.

GCF(10312,10320) = 8
LCM(10312,10320) = ( 10312 × 10320) / 8
LCM(10312,10320) = 106419840 / 8
LCM(10312,10320) = 13302480

Properties of LCM 10312 and 10320

(i) The LCM of 10320 and 10312 is associative

LCM of 10312 and 10320 = LCM of 10320 and 10312

Related Least Common Multiples of 10312

Related Least Common Multiples of 10320

Frequently Asked Questions on LCM of 10312 and 10320

1. What is the LCM of 10312 and 10320?

Answer: LCM of 10312 and 10320 is 13302480.

2. What are the Factors of 10312?

Answer: Factors of 10312 are 1, 2, 4, 8, 1289, 2578, 5156, 10312. There are 8 integers that are factors of 10312. The greatest factor of 10312 is 10312.

3. What are the Factors of 10320?

Answer: Factors of 10320 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 43, 48, 60, 80, 86, 120, 129, 172, 215, 240, 258, 344, 430, 516, 645, 688, 860, 1032, 1290, 1720, 2064, 2580, 3440, 5160, 10320. There are 40 integers that are factors of 10320. The greatest factor of 10320 is 10320.

4. How to Find the LCM of 10312 and 10320?

Answer:

Least Common Multiple of 10312 and 10320 = 13302480

Step 1: Find the prime factorization of 10312

10312 = 2 x 2 x 2 x 1289

Step 2: Find the prime factorization of 10320

10320 = 2 x 2 x 2 x 2 x 3 x 5 x 43

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

LCM = 13302480 = 2 x 2 x 2 x 2 x 3 x 5 x 43 x 1289

Step 4: Therefore, the least common multiple of 10312 and 10320 is 13302480.