Least Common Multiple of 66998 and 67002

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

• Least Common Multiple of 66998 and 67002 by Prime method
• Least Common Multiple of 66998 and 67002 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 66998 and 67002. First we will calculate the prime factors of 66998 and 67002.

Prime Factorization of 66998

Prime factors of 66998 are 2, 139,241. Prime factorization of 66998 in exponential form is:

66998 = 2¹×139¹×241¹

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

Now multiplying the highest exponent prime factors to calculate the LCM of 66998 and 67002.

LCM(66998,67002) = 2¹×3¹×13¹×139¹×241¹×859¹
LCM(66998,67002) = 2244499998

Factors of 66998

List of positive integer factors of 66998 that divides 66998 without a remainder.

1, 2, 139, 241, 278, 482, 33499, 66998

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

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 66998 and 67002, than apply into the LCM equation.

GCF(66998,67002) = 2
LCM(66998,67002) = ( 66998 × 67002) / 2
LCM(66998,67002) = 4488999996 / 2
LCM(66998,67002) = 2244499998

(i) The LCM of 67002 and 66998 is associative

LCM of 66998 and 67002 = LCM of 67002 and 66998

1. What is the LCM of 66998 and 67002?

Answer: LCM of 66998 and 67002 is 2244499998.

2. What are the Factors of 66998?

Answer: Factors of 66998 are 1, 2, 139, 241, 278, 482, 33499, 66998. There are 8 integers that are factors of 66998. The greatest factor of 66998 is 66998.

3. 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.

4. How to Find the LCM of 66998 and 67002?

Answer:

Least Common Multiple of 66998 and 67002 = 2244499998

Step 1: Find the prime factorization of 66998

66998 = 2 x 139 x 241

Step 2: Find the prime factorization of 67002

67002 = 2 x 3 x 13 x 859

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

LCM = 2244499998 = 2 x 3 x 13 x 139 x 241 x 859

Step 4: Therefore, the least common multiple of 66998 and 67002 is 2244499998.