Least Common Multiple of 31426 and 31430

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

• Least Common Multiple of 31426 and 31430 by Prime method
• Least Common Multiple of 31426 and 31430 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31426 and 31430. First we will calculate the prime factors of 31426 and 31430.

Prime Factorization of 31426

Prime factors of 31426 are 2, 19,827. Prime factorization of 31426 in exponential form is:

31426 = 2¹×19¹×827¹

Prime Factorization of 31430

Prime factors of 31430 are 2, 5, 7,449. Prime factorization of 31430 in exponential form is:

31430 = 2¹×5¹×7¹×449¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31426 and 31430.

LCM(31426,31430) = 2¹×5¹×7¹×19¹×449¹×827¹
LCM(31426,31430) = 493859590

Factors of 31426

List of positive integer factors of 31426 that divides 31426 without a remainder.

1, 2, 19, 38, 827, 1654, 15713, 31426

Factors of 31430

List of positive integer factors of 31430 that divides 31430 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 449, 898, 2245, 3143, 4490, 6286, 15715, 31430

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31426 and 31430, than apply into the LCM equation.

GCF(31426,31430) = 2
LCM(31426,31430) = ( 31426 × 31430) / 2
LCM(31426,31430) = 987719180 / 2
LCM(31426,31430) = 493859590

(i) The LCM of 31430 and 31426 is associative

LCM of 31426 and 31430 = LCM of 31430 and 31426

1. What is the LCM of 31426 and 31430?

Answer: LCM of 31426 and 31430 is 493859590.

2. What are the Factors of 31426?

Answer: Factors of 31426 are 1, 2, 19, 38, 827, 1654, 15713, 31426. There are 8 integers that are factors of 31426. The greatest factor of 31426 is 31426.

3. What are the Factors of 31430?

Answer: Factors of 31430 are 1, 2, 5, 7, 10, 14, 35, 70, 449, 898, 2245, 3143, 4490, 6286, 15715, 31430. There are 16 integers that are factors of 31430. The greatest factor of 31430 is 31430.

4. How to Find the LCM of 31426 and 31430?

Answer:

Least Common Multiple of 31426 and 31430 = 493859590

Step 1: Find the prime factorization of 31426

31426 = 2 x 19 x 827

Step 2: Find the prime factorization of 31430

31430 = 2 x 5 x 7 x 449

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

LCM = 493859590 = 2 x 5 x 7 x 19 x 449 x 827

Step 4: Therefore, the least common multiple of 31426 and 31430 is 493859590.