Least Common Multiple of 10104 and 10112

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10104 and 10112 the smallest integer that is 12771456 that is divisible by both numbers.

Least Common Multiple (LCM) of 10104 and 10112 is 12771456.

LCM(10104,10112) = 12771456

LCM of 10104 and 10112

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

LCM of:
and

Least Common Multiple of 10104 and 10112

LCM of 10104 and 10112 is 12771456

Least common multiple can be found by multiplying the highest exponent prime factors of 10104 and 10112. First we will calculate the prime factors of 10104 and 10112.

Prime Factorization of 10104


2 10104
2 5052
2 2526
3 1263
421 421
1

Prime factors of 10104 are 2, 3,421. Prime factorization of 10104 in exponential form is:

10104 = 23×31×4211

Prime Factorization of 10112


2 10112
2 5056
2 2528
2 1264
2 632
2 316
2 158
79 79
1

Prime factors of 10112 are 2,79. Prime factorization of 10112 in exponential form is:

10112 = 27×791

Now multiplying the highest exponent prime factors to calculate the LCM of 10104 and 10112.

LCM(10104,10112) = 27×31×791×4211
LCM(10104,10112) = 12771456

Factors of 10104

List of positive integer factors of 10104 that divides 10104 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 421, 842, 1263, 1684, 2526, 3368, 5052, 10104

Factors of 10112

List of positive integer factors of 10112 that divides 10112 without a remainder.

1, 2, 4, 8, 16, 32, 64, 79, 128, 158, 316, 632, 1264, 2528, 5056, 10112

Least Common Multiple of 10104 and 10112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10104 and 10112, than apply into the LCM equation.

GCF(10104,10112) = 8
LCM(10104,10112) = ( 10104 × 10112) / 8
LCM(10104,10112) = 102171648 / 8
LCM(10104,10112) = 12771456

Properties of LCM 10104 and 10112

(i) The LCM of 10112 and 10104 is associative

LCM of 10104 and 10112 = LCM of 10112 and 10104

Related Least Common Multiples of 10104

Related Least Common Multiples of 10112

Frequently Asked Questions on LCM of 10104 and 10112

1. What is the LCM of 10104 and 10112?

Answer: LCM of 10104 and 10112 is 12771456.

2. What are the Factors of 10104?

Answer: Factors of 10104 are 1, 2, 3, 4, 6, 8, 12, 24, 421, 842, 1263, 1684, 2526, 3368, 5052, 10104. There are 16 integers that are factors of 10104. The greatest factor of 10104 is 10104.

3. What are the Factors of 10112?

Answer: Factors of 10112 are 1, 2, 4, 8, 16, 32, 64, 79, 128, 158, 316, 632, 1264, 2528, 5056, 10112. There are 16 integers that are factors of 10112. The greatest factor of 10112 is 10112.

4. How to Find the LCM of 10104 and 10112?

Answer:

Least Common Multiple of 10104 and 10112 = 12771456

Step 1: Find the prime factorization of 10104

10104 = 2 x 2 x 2 x 3 x 421

Step 2: Find the prime factorization of 10112

10112 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 79

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

LCM = 12771456 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 79 x 421

Step 4: Therefore, the least common multiple of 10104 and 10112 is 12771456.