Least Common Multiple of 1008 and 1016

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 1016 the smallest integer that is 128016 that is divisible by both numbers.

Least Common Multiple (LCM) of 1008 and 1016 is 128016.

LCM(1008,1016) = 128016

LCM of 1008 and 1016

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

LCM of:
and

Least Common Multiple of 1008 and 1016

LCM of 1008 and 1016 is 128016

Least common multiple can be found by multiplying the highest exponent prime factors of 1008 and 1016. First we will calculate the prime factors of 1008 and 1016.

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 1016


2 1016
2 508
2 254
127 127
1

Prime factors of 1016 are 2,127. Prime factorization of 1016 in exponential form is:

1016 = 23×1271

Now multiplying the highest exponent prime factors to calculate the LCM of 1008 and 1016.

LCM(1008,1016) = 24×32×71×1271
LCM(1008,1016) = 128016

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 1016

List of positive integer factors of 1016 that divides 1016 without a remainder.

1, 2, 4, 8, 127, 254, 508, 1016

Least Common Multiple of 1008 and 1016 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 1016, than apply into the LCM equation.

GCF(1008,1016) = 8
LCM(1008,1016) = ( 1008 × 1016) / 8
LCM(1008,1016) = 1024128 / 8
LCM(1008,1016) = 128016

Properties of LCM 1008 and 1016

(i) The LCM of 1016 and 1008 is associative

LCM of 1008 and 1016 = LCM of 1016 and 1008

Related Least Common Multiples of 1008

Related Least Common Multiples of 1016

Frequently Asked Questions on LCM of 1008 and 1016

1. What is the LCM of 1008 and 1016?

Answer: LCM of 1008 and 1016 is 128016.

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 1016?

Answer: Factors of 1016 are 1, 2, 4, 8, 127, 254, 508, 1016. There are 8 integers that are factors of 1016. The greatest factor of 1016 is 1016.

4. How to Find the LCM of 1008 and 1016?

Answer:

Least Common Multiple of 1008 and 1016 = 128016

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 1016

1016 = 2 x 2 x 2 x 127

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

LCM = 128016 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 127

Step 4: Therefore, the least common multiple of 1008 and 1016 is 128016.