Least Common Multiple of 25 and 26

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

• Least Common Multiple of 25 and 26 by Prime method
• Least Common Multiple of 25 and 26 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 25 and 26. First we will calculate the prime factors of 25 and 26.

Prime Factorization of 25

Prime factors of 25 are 5. Prime factorization of 25 in exponential form is:

25 = 5²

Prime Factorization of 26

Prime factors of 26 are 2,13. Prime factorization of 26 in exponential form is:

26 = 2¹×13¹

Now multiplying the highest exponent prime factors to calculate the LCM of 25 and 26.

LCM(25,26) = 2¹×5²×13¹
LCM(25,26) = 650

Factors of 25

List of positive integer factors of 25 that divides 25 without a remainder.

1, 5, 25

Factors of 26

List of positive integer factors of 26 that divides 26 without a remainder.

1, 2, 13, 26

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25 and 26, than apply into the LCM equation.

GCF(25,26) = 1
LCM(25,26) = ( 25 × 26) / 1
LCM(25,26) = 650 / 1
LCM(25,26) = 650

(i) The LCM of 26 and 25 is associative

LCM of 25 and 26 = LCM of 26 and 25

1. What is the LCM of 25 and 26?

Answer: LCM of 25 and 26 is 650.

2. What are the Factors of 25?

Answer: Factors of 25 are 1, 5, 25. There are 3 integers that are factors of 25. The greatest factor of 25 is 25.

3. What are the Factors of 26?

Answer: Factors of 26 are 1, 2, 13, 26. There are 4 integers that are factors of 26. The greatest factor of 26 is 26.

4. How to Find the LCM of 25 and 26?

Answer:

Least Common Multiple of 25 and 26 = 650

Step 1: Find the prime factorization of 25

25 = 5 x 5

Step 2: Find the prime factorization of 26

26 = 2 x 13

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

LCM = 650 = 2 x 5 x 5 x 13

Step 4: Therefore, the least common multiple of 25 and 26 is 650.