Least Common Multiple of 67007 and 67012

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

• Least Common Multiple of 67007 and 67012 by Prime method
• Least Common Multiple of 67007 and 67012 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 67007 and 67012. First we will calculate the prime factors of 67007 and 67012.

Prime Factorization of 67007

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

67007 = 37¹×1811¹

Prime Factorization of 67012

Prime factors of 67012 are 2, 11,1523. Prime factorization of 67012 in exponential form is:

67012 = 2²×11¹×1523¹

Now multiplying the highest exponent prime factors to calculate the LCM of 67007 and 67012.

LCM(67007,67012) = 2²×11¹×37¹×1523¹×1811¹
LCM(67007,67012) = 4490273084

Factors of 67007

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

1, 37, 1811, 67007

Factors of 67012

List of positive integer factors of 67012 that divides 67012 without a remainder.

1, 2, 4, 11, 22, 44, 1523, 3046, 6092, 16753, 33506, 67012

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67007 and 67012, than apply into the LCM equation.

GCF(67007,67012) = 1
LCM(67007,67012) = ( 67007 × 67012) / 1
LCM(67007,67012) = 4490273084 / 1
LCM(67007,67012) = 4490273084

(i) The LCM of 67012 and 67007 is associative

LCM of 67007 and 67012 = LCM of 67012 and 67007

1. What is the LCM of 67007 and 67012?

Answer: LCM of 67007 and 67012 is 4490273084.

2. 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.

3. What are the Factors of 67012?

Answer: Factors of 67012 are 1, 2, 4, 11, 22, 44, 1523, 3046, 6092, 16753, 33506, 67012. There are 12 integers that are factors of 67012. The greatest factor of 67012 is 67012.

4. How to Find the LCM of 67007 and 67012?

Answer:

Least Common Multiple of 67007 and 67012 = 4490273084

Step 1: Find the prime factorization of 67007

67007 = 37 x 1811

Step 2: Find the prime factorization of 67012

67012 = 2 x 2 x 11 x 1523

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

LCM = 4490273084 = 2 x 2 x 11 x 37 x 1523 x 1811

Step 4: Therefore, the least common multiple of 67007 and 67012 is 4490273084.