Least Common Multiple of 67002 and 67008

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 67002 and 67008 the smallest integer that is 748278336 that is divisible by both numbers.

Least Common Multiple (LCM) of 67002 and 67008 is 748278336.

LCM(67002,67008) = 748278336

LCM of 67002 and 67008

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

LCM of:
and

Least Common Multiple of 67002 and 67008

LCM of 67002 and 67008 is 748278336

Least common multiple can be found by multiplying the highest exponent prime factors of 67002 and 67008. First we will calculate the prime factors of 67002 and 67008.

Prime Factorization of 67002


2 67002
3 33501
13 11167
859 859
1

Prime factors of 67002 are 2, 3, 13,859. Prime factorization of 67002 in exponential form is:

67002 = 21×31×131×8591

Prime Factorization of 67008


2 67008
2 33504
2 16752
2 8376
2 4188
2 2094
3 1047
349 349
1

Prime factors of 67008 are 2, 3,349. Prime factorization of 67008 in exponential form is:

67008 = 26×31×3491

Now multiplying the highest exponent prime factors to calculate the LCM of 67002 and 67008.

LCM(67002,67008) = 26×31×131×3491×8591
LCM(67002,67008) = 748278336

Factors of 67002

List of positive integer factors of 67002 that divides 67002 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 859, 1718, 2577, 5154, 11167, 22334, 33501, 67002

Factors of 67008

List of positive integer factors of 67008 that divides 67008 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 349, 698, 1047, 1396, 2094, 2792, 4188, 5584, 8376, 11168, 16752, 22336, 33504, 67008

Least Common Multiple of 67002 and 67008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67002 and 67008, than apply into the LCM equation.

GCF(67002,67008) = 6
LCM(67002,67008) = ( 67002 × 67008) / 6
LCM(67002,67008) = 4489670016 / 6
LCM(67002,67008) = 748278336

Properties of LCM 67002 and 67008

(i) The LCM of 67008 and 67002 is associative

LCM of 67002 and 67008 = LCM of 67008 and 67002

Related Least Common Multiples of 67002

Related Least Common Multiples of 67008

Frequently Asked Questions on LCM of 67002 and 67008

1. What is the LCM of 67002 and 67008?

Answer: LCM of 67002 and 67008 is 748278336.

2. What are the Factors of 67002?

Answer: Factors of 67002 are 1, 2, 3, 6, 13, 26, 39, 78, 859, 1718, 2577, 5154, 11167, 22334, 33501, 67002. There are 16 integers that are factors of 67002. The greatest factor of 67002 is 67002.

3. What are the Factors of 67008?

Answer: Factors of 67008 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 349, 698, 1047, 1396, 2094, 2792, 4188, 5584, 8376, 11168, 16752, 22336, 33504, 67008. There are 28 integers that are factors of 67008. The greatest factor of 67008 is 67008.

4. How to Find the LCM of 67002 and 67008?

Answer:

Least Common Multiple of 67002 and 67008 = 748278336

Step 1: Find the prime factorization of 67002

67002 = 2 x 3 x 13 x 859

Step 2: Find the prime factorization of 67008

67008 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 349

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

LCM = 748278336 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 349 x 859

Step 4: Therefore, the least common multiple of 67002 and 67008 is 748278336.