Least Common Multiple of 10142 and 10149

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

• Least Common Multiple of 10142 and 10149 by Prime method
• Least Common Multiple of 10142 and 10149 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10142 and 10149. First we will calculate the prime factors of 10142 and 10149.

Prime Factorization of 10142

Prime factors of 10142 are 2, 11,461. Prime factorization of 10142 in exponential form is:

10142 = 2¹×11¹×461¹

Prime Factorization of 10149

Prime factors of 10149 are 3, 17,199. Prime factorization of 10149 in exponential form is:

10149 = 3¹×17¹×199¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10142 and 10149.

LCM(10142,10149) = 2¹×3¹×11¹×17¹×199¹×461¹
LCM(10142,10149) = 102931158

Factors of 10142

List of positive integer factors of 10142 that divides 10142 without a remainder.

1, 2, 11, 22, 461, 922, 5071, 10142

Factors of 10149

List of positive integer factors of 10149 that divides 10149 without a remainder.

1, 3, 17, 51, 199, 597, 3383, 10149

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10142 and 10149, than apply into the LCM equation.

GCF(10142,10149) = 1
LCM(10142,10149) = ( 10142 × 10149) / 1
LCM(10142,10149) = 102931158 / 1
LCM(10142,10149) = 102931158

(i) The LCM of 10149 and 10142 is associative

LCM of 10142 and 10149 = LCM of 10149 and 10142

1. What is the LCM of 10142 and 10149?

Answer: LCM of 10142 and 10149 is 102931158.

2. What are the Factors of 10142?

Answer: Factors of 10142 are 1, 2, 11, 22, 461, 922, 5071, 10142. There are 8 integers that are factors of 10142. The greatest factor of 10142 is 10142.

3. What are the Factors of 10149?

Answer: Factors of 10149 are 1, 3, 17, 51, 199, 597, 3383, 10149. There are 8 integers that are factors of 10149. The greatest factor of 10149 is 10149.

4. How to Find the LCM of 10142 and 10149?

Answer:

Least Common Multiple of 10142 and 10149 = 102931158

Step 1: Find the prime factorization of 10142

10142 = 2 x 11 x 461

Step 2: Find the prime factorization of 10149

10149 = 3 x 17 x 199

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

LCM = 102931158 = 2 x 3 x 11 x 17 x 199 x 461

Step 4: Therefore, the least common multiple of 10142 and 10149 is 102931158.