Least Common Multiple of 41 and 69

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

• Least Common Multiple of 41 and 69 by Prime method
• Least Common Multiple of 41 and 69 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 41 and 69. First we will calculate the prime factors of 41 and 69.

Prime Factorization of 41

Prime factors of 41 are 41. Prime factorization of 41 in exponential form is:

41 = 41¹

Prime Factorization of 69

Prime factors of 69 are 3,23. Prime factorization of 69 in exponential form is:

69 = 3¹×23¹

Now multiplying the highest exponent prime factors to calculate the LCM of 41 and 69.

LCM(41,69) = 3¹×23¹×41¹
LCM(41,69) = 2829

Factors of 41

List of positive integer factors of 41 that divides 41 without a remainder.

1, 41

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1, 3, 23, 69

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 41 and 69, than apply into the LCM equation.

GCF(41,69) = 1
LCM(41,69) = ( 41 × 69) / 1
LCM(41,69) = 2829 / 1
LCM(41,69) = 2829

(i) The LCM of 69 and 41 is associative

LCM of 41 and 69 = LCM of 69 and 41

1. What is the LCM of 41 and 69?

Answer: LCM of 41 and 69 is 2829.

2. What are the Factors of 41?

Answer: Factors of 41 are 1, 41. There are 2 integers that are factors of 41. The greatest factor of 41 is 41.

3. What are the Factors of 69?

Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.

4. How to Find the LCM of 41 and 69?

Answer:

Least Common Multiple of 41 and 69 = 2829

Step 1: Find the prime factorization of 41

41 = 41

Step 2: Find the prime factorization of 69

69 = 3 x 23

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

LCM = 2829 = 3 x 23 x 41

Step 4: Therefore, the least common multiple of 41 and 69 is 2829.