Least Common Multiple of 67002 and 67006

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

• Least Common Multiple of 67002 and 67006 by Prime method
• Least Common Multiple of 67002 and 67006 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 67002 and 67006. First we will calculate the prime factors of 67002 and 67006.

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 67006

Prime factors of 67006 are 2,33503. Prime factorization of 67006 in exponential form is:

67006 = 2¹×33503¹

Now multiplying the highest exponent prime factors to calculate the LCM of 67002 and 67006.

LCM(67002,67006) = 2¹×3¹×13¹×859¹×33503¹
LCM(67002,67006) = 2244768006

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 67006

List of positive integer factors of 67006 that divides 67006 without a remainder.

1, 2, 33503, 67006

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67002 and 67006, than apply into the LCM equation.

GCF(67002,67006) = 2
LCM(67002,67006) = ( 67002 × 67006) / 2
LCM(67002,67006) = 4489536012 / 2
LCM(67002,67006) = 2244768006

(i) The LCM of 67006 and 67002 is associative

LCM of 67002 and 67006 = LCM of 67006 and 67002

1. What is the LCM of 67002 and 67006?

Answer: LCM of 67002 and 67006 is 2244768006.

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 67006?

Answer: Factors of 67006 are 1, 2, 33503, 67006. There are 4 integers that are factors of 67006. The greatest factor of 67006 is 67006.

4. How to Find the LCM of 67002 and 67006?

Answer:

Least Common Multiple of 67002 and 67006 = 2244768006

Step 1: Find the prime factorization of 67002

67002 = 2 x 3 x 13 x 859

Step 2: Find the prime factorization of 67006

67006 = 2 x 33503

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

LCM = 2244768006 = 2 x 3 x 13 x 859 x 33503

Step 4: Therefore, the least common multiple of 67002 and 67006 is 2244768006.