Least Common Multiple of 1008 and 1015

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1008 and 1015 the smallest integer that is 146160 that is divisible by both numbers.

Least Common Multiple (LCM) of 1008 and 1015 is 146160.

LCM(1008,1015) = 146160

LCM of 1008 and 1015

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

LCM of:
and

Least Common Multiple of 1008 and 1015

LCM of 1008 and 1015 is 146160

Least common multiple can be found by multiplying the highest exponent prime factors of 1008 and 1015. First we will calculate the prime factors of 1008 and 1015.

Prime Factorization of 1008


2 1008
2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 1008 are 2, 3,7. Prime factorization of 1008 in exponential form is:

1008 = 24×32×71

Prime Factorization of 1015


5 1015
7 203
29 29
1

Prime factors of 1015 are 5, 7,29. Prime factorization of 1015 in exponential form is:

1015 = 51×71×291

Now multiplying the highest exponent prime factors to calculate the LCM of 1008 and 1015.

LCM(1008,1015) = 24×32×51×71×291
LCM(1008,1015) = 146160

Factors of 1008

List of positive integer factors of 1008 that divides 1008 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008

Factors of 1015

List of positive integer factors of 1015 that divides 1015 without a remainder.

1, 5, 7, 29, 35, 145, 203, 1015

Least Common Multiple of 1008 and 1015 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1008 and 1015, than apply into the LCM equation.

GCF(1008,1015) = 7
LCM(1008,1015) = ( 1008 × 1015) / 7
LCM(1008,1015) = 1023120 / 7
LCM(1008,1015) = 146160

Properties of LCM 1008 and 1015

(i) The LCM of 1015 and 1008 is associative

LCM of 1008 and 1015 = LCM of 1015 and 1008

Related Least Common Multiples of 1008

Related Least Common Multiples of 1015

Frequently Asked Questions on LCM of 1008 and 1015

1. What is the LCM of 1008 and 1015?

Answer: LCM of 1008 and 1015 is 146160.

2. What are the Factors of 1008?

Answer: Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. There are 30 integers that are factors of 1008. The greatest factor of 1008 is 1008.

3. What are the Factors of 1015?

Answer: Factors of 1015 are 1, 5, 7, 29, 35, 145, 203, 1015. There are 8 integers that are factors of 1015. The greatest factor of 1015 is 1015.

4. How to Find the LCM of 1008 and 1015?

Answer:

Least Common Multiple of 1008 and 1015 = 146160

Step 1: Find the prime factorization of 1008

1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 1015

1015 = 5 x 7 x 29

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

LCM = 146160 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 29

Step 4: Therefore, the least common multiple of 1008 and 1015 is 146160.