Least Common Multiple of 66997 and 67001

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

• Least Common Multiple of 66997 and 67001 by Prime method
• Least Common Multiple of 66997 and 67001 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 66997 and 67001. First we will calculate the prime factors of 66997 and 67001.

Prime Factorization of 66997

Prime factors of 66997 are 7, 17,563. Prime factorization of 66997 in exponential form is:

66997 = 7¹×17¹×563¹

Prime Factorization of 67001

Prime factors of 67001 are 11,6091. Prime factorization of 67001 in exponential form is:

67001 = 11¹×6091¹

Now multiplying the highest exponent prime factors to calculate the LCM of 66997 and 67001.

LCM(66997,67001) = 7¹×11¹×17¹×563¹×6091¹
LCM(66997,67001) = 4488865997

Factors of 66997

List of positive integer factors of 66997 that divides 66997 without a remainder.

1, 7, 17, 119, 563, 3941, 9571, 66997

Factors of 67001

List of positive integer factors of 67001 that divides 67001 without a remainder.

1, 11, 6091, 67001

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 66997 and 67001, than apply into the LCM equation.

GCF(66997,67001) = 1
LCM(66997,67001) = ( 66997 × 67001) / 1
LCM(66997,67001) = 4488865997 / 1
LCM(66997,67001) = 4488865997

(i) The LCM of 67001 and 66997 is associative

LCM of 66997 and 67001 = LCM of 67001 and 66997

1. What is the LCM of 66997 and 67001?

Answer: LCM of 66997 and 67001 is 4488865997.

2. What are the Factors of 66997?

Answer: Factors of 66997 are 1, 7, 17, 119, 563, 3941, 9571, 66997. There are 8 integers that are factors of 66997. The greatest factor of 66997 is 66997.

3. What are the Factors of 67001?

Answer: Factors of 67001 are 1, 11, 6091, 67001. There are 4 integers that are factors of 67001. The greatest factor of 67001 is 67001.

4. How to Find the LCM of 66997 and 67001?

Answer:

Least Common Multiple of 66997 and 67001 = 4488865997

Step 1: Find the prime factorization of 66997

66997 = 7 x 17 x 563

Step 2: Find the prime factorization of 67001

67001 = 11 x 6091

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

LCM = 4488865997 = 7 x 11 x 17 x 563 x 6091

Step 4: Therefore, the least common multiple of 66997 and 67001 is 4488865997.