Least Common Multiple of 34 and 41

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

• Least Common Multiple of 34 and 41 by Prime method
• Least Common Multiple of 34 and 41 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 41. First we will calculate the prime factors of 34 and 41.

Prime Factorization of 34

Prime factors of 34 are 2,17. Prime factorization of 34 in exponential form is:

34 = 2¹×17¹

Prime Factorization of 41

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

41 = 41¹

Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 41.

LCM(34,41) = 2¹×17¹×41¹
LCM(34,41) = 1394

Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1, 2, 17, 34

Factors of 41

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

1, 41

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34 and 41, than apply into the LCM equation.

GCF(34,41) = 1
LCM(34,41) = ( 34 × 41) / 1
LCM(34,41) = 1394 / 1
LCM(34,41) = 1394

(i) The LCM of 41 and 34 is associative

LCM of 34 and 41 = LCM of 41 and 34

1. What is the LCM of 34 and 41?

Answer: LCM of 34 and 41 is 1394.

2. What are the Factors of 34?

Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.

3. 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.

4. How to Find the LCM of 34 and 41?

Answer:

Least Common Multiple of 34 and 41 = 1394

Step 1: Find the prime factorization of 34

34 = 2 x 17

Step 2: Find the prime factorization of 41

41 = 41

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

LCM = 1394 = 2 x 17 x 41

Step 4: Therefore, the least common multiple of 34 and 41 is 1394.