Least Common Multiple of 416 and 419

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 416 and 419 the smallest integer that is 174304 that is divisible by both numbers.

Least Common Multiple (LCM) of 416 and 419 is 174304.

LCM(416,419) = 174304

LCM of 416 and 419

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

LCM of:
and

Least Common Multiple of 416 and 419

LCM of 416 and 419 is 174304

Least common multiple can be found by multiplying the highest exponent prime factors of 416 and 419. First we will calculate the prime factors of 416 and 419.

Prime Factorization of 416


2 416
2 208
2 104
2 52
2 26
13 13
1

Prime factors of 416 are 2,13. Prime factorization of 416 in exponential form is:

416 = 25×131

Prime Factorization of 419


419 419
1

Prime factors of 419 are 419. Prime factorization of 419 in exponential form is:

419 = 4191

Now multiplying the highest exponent prime factors to calculate the LCM of 416 and 419.

LCM(416,419) = 25×131×4191
LCM(416,419) = 174304

Factors of 416

List of positive integer factors of 416 that divides 416 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

Factors of 419

List of positive integer factors of 419 that divides 419 without a remainder.

1, 419

Least Common Multiple of 416 and 419 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 416 and 419, than apply into the LCM equation.

GCF(416,419) = 1
LCM(416,419) = ( 416 × 419) / 1
LCM(416,419) = 174304 / 1
LCM(416,419) = 174304

Properties of LCM 416 and 419

(i) The LCM of 419 and 416 is associative

LCM of 416 and 419 = LCM of 419 and 416

Related Least Common Multiples of 416

Related Least Common Multiples of 419

Frequently Asked Questions on LCM of 416 and 419

1. What is the LCM of 416 and 419?

Answer: LCM of 416 and 419 is 174304.

2. What are the Factors of 416?

Answer: Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416. There are 12 integers that are factors of 416. The greatest factor of 416 is 416.

3. What are the Factors of 419?

Answer: Factors of 419 are 1, 419. There are 2 integers that are factors of 419. The greatest factor of 419 is 419.

4. How to Find the LCM of 416 and 419?

Answer:

Least Common Multiple of 416 and 419 = 174304

Step 1: Find the prime factorization of 416

416 = 2 x 2 x 2 x 2 x 2 x 13

Step 2: Find the prime factorization of 419

419 = 419

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

LCM = 174304 = 2 x 2 x 2 x 2 x 2 x 13 x 419

Step 4: Therefore, the least common multiple of 416 and 419 is 174304.