Least Common Multiple of 10112 and 10117

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 10117 the smallest integer that is 102303104 that is divisible by both numbers.

Least Common Multiple (LCM) of 10112 and 10117 is 102303104.

LCM(10112,10117) = 102303104

LCM of 10112 and 10117

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

LCM of:
and

Least Common Multiple of 10112 and 10117

LCM of 10112 and 10117 is 102303104

Least common multiple can be found by multiplying the highest exponent prime factors of 10112 and 10117. First we will calculate the prime factors of 10112 and 10117.

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 10117


67 10117
151 151
1

Prime factors of 10117 are 67,151. Prime factorization of 10117 in exponential form is:

10117 = 671×1511

Now multiplying the highest exponent prime factors to calculate the LCM of 10112 and 10117.

LCM(10112,10117) = 27×671×791×1511
LCM(10112,10117) = 102303104

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 10117

List of positive integer factors of 10117 that divides 10117 without a remainder.

1, 67, 151, 10117

Least Common Multiple of 10112 and 10117 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 10117, than apply into the LCM equation.

GCF(10112,10117) = 1
LCM(10112,10117) = ( 10112 × 10117) / 1
LCM(10112,10117) = 102303104 / 1
LCM(10112,10117) = 102303104

Properties of LCM 10112 and 10117

(i) The LCM of 10117 and 10112 is associative

LCM of 10112 and 10117 = LCM of 10117 and 10112

Related Least Common Multiples of 10112

Related Least Common Multiples of 10117

Frequently Asked Questions on LCM of 10112 and 10117

1. What is the LCM of 10112 and 10117?

Answer: LCM of 10112 and 10117 is 102303104.

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 10117?

Answer: Factors of 10117 are 1, 67, 151, 10117. There are 4 integers that are factors of 10117. The greatest factor of 10117 is 10117.

4. How to Find the LCM of 10112 and 10117?

Answer:

Least Common Multiple of 10112 and 10117 = 102303104

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 10117

10117 = 67 x 151

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

LCM = 102303104 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 67 x 79 x 151

Step 4: Therefore, the least common multiple of 10112 and 10117 is 102303104.