Least Common Multiple of 10112 and 10116

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10112 and 10116 the smallest integer that is 25573248 that is divisible by both numbers.

Least Common Multiple (LCM) of 10112 and 10116 is 25573248.

LCM(10112,10116) = 25573248

LCM of 10112 and 10116

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

LCM of:
and

Least Common Multiple of 10112 and 10116

LCM of 10112 and 10116 is 25573248

Least common multiple can be found by multiplying the highest exponent prime factors of 10112 and 10116. First we will calculate the prime factors of 10112 and 10116.

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

Prime Factorization of 10116


2 10116
2 5058
3 2529
3 843
281 281
1

Prime factors of 10116 are 2, 3,281. Prime factorization of 10116 in exponential form is:

10116 = 22×32×2811

Now multiplying the highest exponent prime factors to calculate the LCM of 10112 and 10116.

LCM(10112,10116) = 27×32×791×2811
LCM(10112,10116) = 25573248

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

Factors of 10116

List of positive integer factors of 10116 that divides 10116 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 281, 562, 843, 1124, 1686, 2529, 3372, 5058, 10116

Least Common Multiple of 10112 and 10116 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10112 and 10116, than apply into the LCM equation.

GCF(10112,10116) = 4
LCM(10112,10116) = ( 10112 × 10116) / 4
LCM(10112,10116) = 102292992 / 4
LCM(10112,10116) = 25573248

Properties of LCM 10112 and 10116

(i) The LCM of 10116 and 10112 is associative

LCM of 10112 and 10116 = LCM of 10116 and 10112

Related Least Common Multiples of 10112

Related Least Common Multiples of 10116

Frequently Asked Questions on LCM of 10112 and 10116

1. What is the LCM of 10112 and 10116?

Answer: LCM of 10112 and 10116 is 25573248.

2. 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.

3. What are the Factors of 10116?

Answer: Factors of 10116 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 281, 562, 843, 1124, 1686, 2529, 3372, 5058, 10116. There are 18 integers that are factors of 10116. The greatest factor of 10116 is 10116.

4. How to Find the LCM of 10112 and 10116?

Answer:

Least Common Multiple of 10112 and 10116 = 25573248

Step 1: Find the prime factorization of 10112

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

Step 2: Find the prime factorization of 10116

10116 = 2 x 2 x 3 x 3 x 281

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

LCM = 25573248 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 79 x 281

Step 4: Therefore, the least common multiple of 10112 and 10116 is 25573248.