Least Common Multiple of 66998 and 67005

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

• Least Common Multiple of 66998 and 67005 by Prime method
• Least Common Multiple of 66998 and 67005 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 66998 and 67005. First we will calculate the prime factors of 66998 and 67005.

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 67005

Prime factors of 67005 are 3, 5,1489. Prime factorization of 67005 in exponential form is:

67005 = 3²×5¹×1489¹

Now multiplying the highest exponent prime factors to calculate the LCM of 66998 and 67005.

LCM(66998,67005) = 2¹×3²×5¹×139¹×241¹×1489¹
LCM(66998,67005) = 4489200990

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 67005

List of positive integer factors of 67005 that divides 67005 without a remainder.

1, 3, 5, 9, 15, 45, 1489, 4467, 7445, 13401, 22335, 67005

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 66998 and 67005, than apply into the LCM equation.

GCF(66998,67005) = 1
LCM(66998,67005) = ( 66998 × 67005) / 1
LCM(66998,67005) = 4489200990 / 1
LCM(66998,67005) = 4489200990

(i) The LCM of 67005 and 66998 is associative

LCM of 66998 and 67005 = LCM of 67005 and 66998

1. What is the LCM of 66998 and 67005?

Answer: LCM of 66998 and 67005 is 4489200990.

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 67005?

Answer: Factors of 67005 are 1, 3, 5, 9, 15, 45, 1489, 4467, 7445, 13401, 22335, 67005. There are 12 integers that are factors of 67005. The greatest factor of 67005 is 67005.

4. How to Find the LCM of 66998 and 67005?

Answer:

Least Common Multiple of 66998 and 67005 = 4489200990

Step 1: Find the prime factorization of 66998

66998 = 2 x 139 x 241

Step 2: Find the prime factorization of 67005

67005 = 3 x 3 x 5 x 1489

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

LCM = 4489200990 = 2 x 3 x 3 x 5 x 139 x 241 x 1489

Step 4: Therefore, the least common multiple of 66998 and 67005 is 4489200990.