Least Common Multiple of 9114 and 9120

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9114 and 9120 the smallest integer that is 13853280 that is divisible by both numbers.

Least Common Multiple (LCM) of 9114 and 9120 is 13853280.

LCM(9114,9120) = 13853280

LCM of 9114 and 9120

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

LCM of:
and

Least Common Multiple of 9114 and 9120

LCM of 9114 and 9120 is 13853280

Least common multiple can be found by multiplying the highest exponent prime factors of 9114 and 9120. First we will calculate the prime factors of 9114 and 9120.

Prime Factorization of 9114


2 9114
3 4557
7 1519
7 217
31 31
1

Prime factors of 9114 are 2, 3, 7,31. Prime factorization of 9114 in exponential form is:

9114 = 21×31×72×311

Prime Factorization of 9120


2 9120
2 4560
2 2280
2 1140
2 570
3 285
5 95
19 19
1

Prime factors of 9120 are 2, 3, 5,19. Prime factorization of 9120 in exponential form is:

9120 = 25×31×51×191

Now multiplying the highest exponent prime factors to calculate the LCM of 9114 and 9120.

LCM(9114,9120) = 25×31×51×72×191×311
LCM(9114,9120) = 13853280

Factors of 9114

List of positive integer factors of 9114 that divides 9114 without a remainder.

1, 2, 3, 6, 7, 14, 21, 31, 42, 49, 62, 93, 98, 147, 186, 217, 294, 434, 651, 1302, 1519, 3038, 4557, 9114

Factors of 9120

List of positive integer factors of 9120 that divides 9120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 76, 80, 95, 96, 114, 120, 152, 160, 190, 228, 240, 285, 304, 380, 456, 480, 570, 608, 760, 912, 1140, 1520, 1824, 2280, 3040, 4560, 9120

Least Common Multiple of 9114 and 9120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9114 and 9120, than apply into the LCM equation.

GCF(9114,9120) = 6
LCM(9114,9120) = ( 9114 × 9120) / 6
LCM(9114,9120) = 83119680 / 6
LCM(9114,9120) = 13853280

Properties of LCM 9114 and 9120

(i) The LCM of 9120 and 9114 is associative

LCM of 9114 and 9120 = LCM of 9120 and 9114

Related Least Common Multiples of 9114

Related Least Common Multiples of 9120

Frequently Asked Questions on LCM of 9114 and 9120

1. What is the LCM of 9114 and 9120?

Answer: LCM of 9114 and 9120 is 13853280.

2. What are the Factors of 9114?

Answer: Factors of 9114 are 1, 2, 3, 6, 7, 14, 21, 31, 42, 49, 62, 93, 98, 147, 186, 217, 294, 434, 651, 1302, 1519, 3038, 4557, 9114. There are 24 integers that are factors of 9114. The greatest factor of 9114 is 9114.

3. What are the Factors of 9120?

Answer: Factors of 9120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 76, 80, 95, 96, 114, 120, 152, 160, 190, 228, 240, 285, 304, 380, 456, 480, 570, 608, 760, 912, 1140, 1520, 1824, 2280, 3040, 4560, 9120. There are 48 integers that are factors of 9120. The greatest factor of 9120 is 9120.

4. How to Find the LCM of 9114 and 9120?

Answer:

Least Common Multiple of 9114 and 9120 = 13853280

Step 1: Find the prime factorization of 9114

9114 = 2 x 3 x 7 x 7 x 31

Step 2: Find the prime factorization of 9120

9120 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 19

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

LCM = 13853280 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7 x 19 x 31

Step 4: Therefore, the least common multiple of 9114 and 9120 is 13853280.