Least Common Multiple of 29014 and 29022

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

• Least Common Multiple of 29014 and 29022 by Prime method
• Least Common Multiple of 29014 and 29022 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 29014 and 29022. First we will calculate the prime factors of 29014 and 29022.

Prime Factorization of 29014

Prime factors of 29014 are 2, 89,163. Prime factorization of 29014 in exponential form is:

29014 = 2¹×89¹×163¹

Prime Factorization of 29022

Prime factors of 29022 are 2, 3, 7,691. Prime factorization of 29022 in exponential form is:

29022 = 2¹×3¹×7¹×691¹

Now multiplying the highest exponent prime factors to calculate the LCM of 29014 and 29022.

LCM(29014,29022) = 2¹×3¹×7¹×89¹×163¹×691¹
LCM(29014,29022) = 421022154

Factors of 29014

List of positive integer factors of 29014 that divides 29014 without a remainder.

1, 2, 89, 163, 178, 326, 14507, 29014

Factors of 29022

List of positive integer factors of 29022 that divides 29022 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 691, 1382, 2073, 4146, 4837, 9674, 14511, 29022

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29014 and 29022, than apply into the LCM equation.

GCF(29014,29022) = 2
LCM(29014,29022) = ( 29014 × 29022) / 2
LCM(29014,29022) = 842044308 / 2
LCM(29014,29022) = 421022154

(i) The LCM of 29022 and 29014 is associative

LCM of 29014 and 29022 = LCM of 29022 and 29014

1. What is the LCM of 29014 and 29022?

Answer: LCM of 29014 and 29022 is 421022154.

2. What are the Factors of 29014?

Answer: Factors of 29014 are 1, 2, 89, 163, 178, 326, 14507, 29014. There are 8 integers that are factors of 29014. The greatest factor of 29014 is 29014.

3. What are the Factors of 29022?

Answer: Factors of 29022 are 1, 2, 3, 6, 7, 14, 21, 42, 691, 1382, 2073, 4146, 4837, 9674, 14511, 29022. There are 16 integers that are factors of 29022. The greatest factor of 29022 is 29022.

4. How to Find the LCM of 29014 and 29022?

Answer:

Least Common Multiple of 29014 and 29022 = 421022154

Step 1: Find the prime factorization of 29014

29014 = 2 x 89 x 163

Step 2: Find the prime factorization of 29022

29022 = 2 x 3 x 7 x 691

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

LCM = 421022154 = 2 x 3 x 7 x 89 x 163 x 691

Step 4: Therefore, the least common multiple of 29014 and 29022 is 421022154.