Least Common Multiple of 106 and 110

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 106 and 110 the smallest integer that is 5830 that is divisible by both numbers.

Least Common Multiple (LCM) of 106 and 110 is 5830.

LCM(106,110) = 5830

LCM of 106 and 110

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

LCM of:
and

Least Common Multiple of 106 and 110

LCM of 106 and 110 is 5830

Least common multiple can be found by multiplying the highest exponent prime factors of 106 and 110. First we will calculate the prime factors of 106 and 110.

Prime Factorization of 106


2 106
53 53
1

Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:

106 = 21×531

Prime Factorization of 110


2 110
5 55
11 11
1

Prime factors of 110 are 2, 5,11. Prime factorization of 110 in exponential form is:

110 = 21×51×111

Now multiplying the highest exponent prime factors to calculate the LCM of 106 and 110.

LCM(106,110) = 21×51×111×531
LCM(106,110) = 5830

Factors of 106

List of positive integer factors of 106 that divides 106 without a remainder.

1, 2, 53, 106

Factors of 110

List of positive integer factors of 110 that divides 110 without a remainder.

1, 2, 5, 10, 11, 22, 55, 110

Least Common Multiple of 106 and 110 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 106 and 110, than apply into the LCM equation.

GCF(106,110) = 2
LCM(106,110) = ( 106 × 110) / 2
LCM(106,110) = 11660 / 2
LCM(106,110) = 5830

Properties of LCM 106 and 110

(i) The LCM of 110 and 106 is associative

LCM of 106 and 110 = LCM of 110 and 106

Related Least Common Multiples of 106

Related Least Common Multiples of 110

Frequently Asked Questions on LCM of 106 and 110

1. What is the LCM of 106 and 110?

Answer: LCM of 106 and 110 is 5830.

2. What are the Factors of 106?

Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.

3. What are the Factors of 110?

Answer: Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. There are 8 integers that are factors of 110. The greatest factor of 110 is 110.

4. How to Find the LCM of 106 and 110?

Answer:

Least Common Multiple of 106 and 110 = 5830

Step 1: Find the prime factorization of 106

106 = 2 x 53

Step 2: Find the prime factorization of 110

110 = 2 x 5 x 11

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

LCM = 5830 = 2 x 5 x 11 x 53

Step 4: Therefore, the least common multiple of 106 and 110 is 5830.