Least Common Multiple of 67002 and 67010

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

• Least Common Multiple of 67002 and 67010 by Prime method
• Least Common Multiple of 67002 and 67010 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 67002 and 67010. First we will calculate the prime factors of 67002 and 67010.

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 67010

Prime factors of 67010 are 2, 5,6701. Prime factorization of 67010 in exponential form is:

67010 = 2¹×5¹×6701¹

Now multiplying the highest exponent prime factors to calculate the LCM of 67002 and 67010.

LCM(67002,67010) = 2¹×3¹×5¹×13¹×859¹×6701¹
LCM(67002,67010) = 2244902010

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 67010

List of positive integer factors of 67010 that divides 67010 without a remainder.

1, 2, 5, 10, 6701, 13402, 33505, 67010

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67002 and 67010, than apply into the LCM equation.

GCF(67002,67010) = 2
LCM(67002,67010) = ( 67002 × 67010) / 2
LCM(67002,67010) = 4489804020 / 2
LCM(67002,67010) = 2244902010

(i) The LCM of 67010 and 67002 is associative

LCM of 67002 and 67010 = LCM of 67010 and 67002

1. What is the LCM of 67002 and 67010?

Answer: LCM of 67002 and 67010 is 2244902010.

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 67010?

Answer: Factors of 67010 are 1, 2, 5, 10, 6701, 13402, 33505, 67010. There are 8 integers that are factors of 67010. The greatest factor of 67010 is 67010.

4. How to Find the LCM of 67002 and 67010?

Answer:

Least Common Multiple of 67002 and 67010 = 2244902010

Step 1: Find the prime factorization of 67002

67002 = 2 x 3 x 13 x 859

Step 2: Find the prime factorization of 67010

67010 = 2 x 5 x 6701

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

LCM = 2244902010 = 2 x 3 x 5 x 13 x 859 x 6701

Step 4: Therefore, the least common multiple of 67002 and 67010 is 2244902010.