Least Common Multiple of 104 and 105

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 104 and 105 the smallest integer that is 10920 that is divisible by both numbers.

Least Common Multiple (LCM) of 104 and 105 is 10920.

LCM(104,105) = 10920

LCM of 104 and 105

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

LCM of:
and

Least Common Multiple of 104 and 105

LCM of 104 and 105 is 10920

Least common multiple can be found by multiplying the highest exponent prime factors of 104 and 105. First we will calculate the prime factors of 104 and 105.

Prime Factorization of 104


2 104
2 52
2 26
13 13
1

Prime factors of 104 are 2,13. Prime factorization of 104 in exponential form is:

104 = 23×131

Prime Factorization of 105


3 105
5 35
7 7
1

Prime factors of 105 are 3, 5,7. Prime factorization of 105 in exponential form is:

105 = 31×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 104 and 105.

LCM(104,105) = 23×31×51×71×131
LCM(104,105) = 10920

Factors of 104

List of positive integer factors of 104 that divides 104 without a remainder.

1, 2, 4, 8, 13, 26, 52, 104

Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105

Least Common Multiple of 104 and 105 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 104 and 105, than apply into the LCM equation.

GCF(104,105) = 1
LCM(104,105) = ( 104 × 105) / 1
LCM(104,105) = 10920 / 1
LCM(104,105) = 10920

Properties of LCM 104 and 105

(i) The LCM of 105 and 104 is associative

LCM of 104 and 105 = LCM of 105 and 104

Related Least Common Multiples of 104

Related Least Common Multiples of 105

Frequently Asked Questions on LCM of 104 and 105

1. What is the LCM of 104 and 105?

Answer: LCM of 104 and 105 is 10920.

2. What are the Factors of 104?

Answer: Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104. There are 8 integers that are factors of 104. The greatest factor of 104 is 104.

3. What are the Factors of 105?

Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.

4. How to Find the LCM of 104 and 105?

Answer:

Least Common Multiple of 104 and 105 = 10920

Step 1: Find the prime factorization of 104

104 = 2 x 2 x 2 x 13

Step 2: Find the prime factorization of 105

105 = 3 x 5 x 7

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

LCM = 10920 = 2 x 2 x 2 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 104 and 105 is 10920.