Least Common Multiple of 414 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 414 and 419 the smallest integer that is 173466 that is divisible by both numbers.

Least Common Multiple (LCM) of 414 and 419 is 173466.

LCM(414,419) = 173466

LCM of 414 and 419

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

LCM of:
and

Least Common Multiple of 414 and 419

LCM of 414 and 419 is 173466

Least common multiple can be found by multiplying the highest exponent prime factors of 414 and 419. First we will calculate the prime factors of 414 and 419.

Prime Factorization of 414


2 414
3 207
3 69
23 23
1

Prime factors of 414 are 2, 3,23. Prime factorization of 414 in exponential form is:

414 = 21×32×231

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 414 and 419.

LCM(414,419) = 21×32×231×4191
LCM(414,419) = 173466

Factors of 414

List of positive integer factors of 414 that divides 414 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

Factors of 419

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

1, 419

Least Common Multiple of 414 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 414 and 419, than apply into the LCM equation.

GCF(414,419) = 1
LCM(414,419) = ( 414 × 419) / 1
LCM(414,419) = 173466 / 1
LCM(414,419) = 173466

Properties of LCM 414 and 419

(i) The LCM of 419 and 414 is associative

LCM of 414 and 419 = LCM of 419 and 414

Related Least Common Multiples of 414

Related Least Common Multiples of 419

Frequently Asked Questions on LCM of 414 and 419

1. What is the LCM of 414 and 419?

Answer: LCM of 414 and 419 is 173466.

2. What are the Factors of 414?

Answer: Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414. There are 12 integers that are factors of 414. The greatest factor of 414 is 414.

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 414 and 419?

Answer:

Least Common Multiple of 414 and 419 = 173466

Step 1: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

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 = 173466 = 2 x 3 x 3 x 23 x 419

Step 4: Therefore, the least common multiple of 414 and 419 is 173466.