Least Common Multiple of 6174 and 6180

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6174 and 6180 the smallest integer that is 6359220 that is divisible by both numbers.

Least Common Multiple (LCM) of 6174 and 6180 is 6359220.

LCM(6174,6180) = 6359220

LCM of 6174 and 6180

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

LCM of:
and

Least Common Multiple of 6174 and 6180

LCM of 6174 and 6180 is 6359220

Least common multiple can be found by multiplying the highest exponent prime factors of 6174 and 6180. First we will calculate the prime factors of 6174 and 6180.

Prime Factorization of 6174


2 6174
3 3087
3 1029
7 343
7 49
7 7
1

Prime factors of 6174 are 2, 3,7. Prime factorization of 6174 in exponential form is:

6174 = 21×32×73

Prime Factorization of 6180


2 6180
2 3090
3 1545
5 515
103 103
1

Prime factors of 6180 are 2, 3, 5,103. Prime factorization of 6180 in exponential form is:

6180 = 22×31×51×1031

Now multiplying the highest exponent prime factors to calculate the LCM of 6174 and 6180.

LCM(6174,6180) = 22×32×51×73×1031
LCM(6174,6180) = 6359220

Factors of 6174

List of positive integer factors of 6174 that divides 6174 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087, 6174

Factors of 6180

List of positive integer factors of 6180 that divides 6180 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 103, 206, 309, 412, 515, 618, 1030, 1236, 1545, 2060, 3090, 6180

Least Common Multiple of 6174 and 6180 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6174 and 6180, than apply into the LCM equation.

GCF(6174,6180) = 6
LCM(6174,6180) = ( 6174 × 6180) / 6
LCM(6174,6180) = 38155320 / 6
LCM(6174,6180) = 6359220

Properties of LCM 6174 and 6180

(i) The LCM of 6180 and 6174 is associative

LCM of 6174 and 6180 = LCM of 6180 and 6174

Related Least Common Multiples of 6174

Related Least Common Multiples of 6180

Frequently Asked Questions on LCM of 6174 and 6180

1. What is the LCM of 6174 and 6180?

Answer: LCM of 6174 and 6180 is 6359220.

2. What are the Factors of 6174?

Answer: Factors of 6174 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087, 6174. There are 24 integers that are factors of 6174. The greatest factor of 6174 is 6174.

3. What are the Factors of 6180?

Answer: Factors of 6180 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 103, 206, 309, 412, 515, 618, 1030, 1236, 1545, 2060, 3090, 6180. There are 24 integers that are factors of 6180. The greatest factor of 6180 is 6180.

4. How to Find the LCM of 6174 and 6180?

Answer:

Least Common Multiple of 6174 and 6180 = 6359220

Step 1: Find the prime factorization of 6174

6174 = 2 x 3 x 3 x 7 x 7 x 7

Step 2: Find the prime factorization of 6180

6180 = 2 x 2 x 3 x 5 x 103

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

LCM = 6359220 = 2 x 2 x 3 x 3 x 5 x 7 x 7 x 7 x 103

Step 4: Therefore, the least common multiple of 6174 and 6180 is 6359220.