Least Common Multiple of 407 and 414
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 407 and 414 the smallest integer that is 168498 that is divisible by both numbers.
Least Common Multiple (LCM) of 407 and 414 is 168498.
LCM(407,414) = 168498
LCM of 407 and 414
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 407 and 414 by Prime method
- Least Common Multiple of 407 and 414 with GCF Formula
LCM of 407 and 414 is 168498
Least common multiple can be found by multiplying the highest exponent prime factors of 407 and 414. First we will calculate the prime factors of 407 and 414.
Prime Factorization of 407
| 11 | 407 |
| 37 | 37 |
| 1 |
Prime factors of 407 are 11,37. Prime factorization of 407 in exponential form is:
407 = 111×371
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
Now multiplying the highest exponent prime factors to calculate the LCM of 407 and 414.
LCM(407,414) = 21×32×111×231×371
LCM(407,414) = 168498
Factors of 407
List of positive integer factors of 407 that divides 407 without a remainder.
1, 11, 37, 407
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
Least Common Multiple of 407 and 414 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 407 and 414, than apply into the LCM equation.
GCF(407,414) = 1
LCM(407,414) = ( 407 × 414) / 1
LCM(407,414) = 168498 / 1
LCM(407,414) = 168498
Properties of LCM 407 and 414
(i) The LCM of 414 and 407 is associative
LCM of 407 and 414 = LCM of 414 and 407
Related Least Common Multiples of 407
Related Least Common Multiples of 414
Frequently Asked Questions on LCM of 407 and 414
1. What is the LCM of 407 and 414?
Answer: LCM of 407 and 414 is 168498.
2. What are the Factors of 407?
Answer: Factors of 407 are 1, 11, 37, 407. There are 4 integers that are factors of 407. The greatest factor of 407 is 407.
3. 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.
4. How to Find the LCM of 407 and 414?
Answer:
Least Common Multiple of 407 and 414 = 168498
Step 1: Find the prime factorization of 407
407 = 11 x 37
Step 2: Find the prime factorization of 414
414 = 2 x 3 x 3 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 168498 = 2 x 3 x 3 x 11 x 23 x 37
Step 4: Therefore, the least common multiple of 407 and 414 is 168498.
