Least Common Multiple of 67002 and 67007

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

• Least Common Multiple of 67002 and 67007 by Prime method
• Least Common Multiple of 67002 and 67007 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 67002 and 67007. First we will calculate the prime factors of 67002 and 67007.

Prime Factorization of 67002

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 67007

Prime factors of 67007 are 37,1811. Prime factorization of 67007 in exponential form is:

67007 = 37¹×1811¹

Now multiplying the highest exponent prime factors to calculate the LCM of 67002 and 67007.

LCM(67002,67007) = 2¹×3¹×13¹×37¹×859¹×1811¹
LCM(67002,67007) = 4489603014

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 67007

List of positive integer factors of 67007 that divides 67007 without a remainder.

1, 37, 1811, 67007

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67002 and 67007, than apply into the LCM equation.

GCF(67002,67007) = 1
LCM(67002,67007) = ( 67002 × 67007) / 1
LCM(67002,67007) = 4489603014 / 1
LCM(67002,67007) = 4489603014

(i) The LCM of 67007 and 67002 is associative

LCM of 67002 and 67007 = LCM of 67007 and 67002

1. What is the LCM of 67002 and 67007?

Answer: LCM of 67002 and 67007 is 4489603014.

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 67007?

Answer: Factors of 67007 are 1, 37, 1811, 67007. There are 4 integers that are factors of 67007. The greatest factor of 67007 is 67007.

4. How to Find the LCM of 67002 and 67007?

Answer:

Least Common Multiple of 67002 and 67007 = 4489603014

Step 1: Find the prime factorization of 67002

67002 = 2 x 3 x 13 x 859

Step 2: Find the prime factorization of 67007

67007 = 37 x 1811

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

LCM = 4489603014 = 2 x 3 x 13 x 37 x 859 x 1811

Step 4: Therefore, the least common multiple of 67002 and 67007 is 4489603014.