Least Common Multiple of 414 and 417
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 417 the smallest integer that is 57546 that is divisible by both numbers.
Least Common Multiple (LCM) of 414 and 417 is 57546.
LCM(414,417) = 57546
LCM of 414 and 417
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 414 and 417 by Prime method
- Least Common Multiple of 414 and 417 with GCF Formula
LCM of 414 and 417 is 57546
Least common multiple can be found by multiplying the highest exponent prime factors of 414 and 417. First we will calculate the prime factors of 414 and 417.
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 417
| 3 | 417 |
| 139 | 139 |
| 1 |
Prime factors of 417 are 3,139. Prime factorization of 417 in exponential form is:
417 = 31×1391
Now multiplying the highest exponent prime factors to calculate the LCM of 414 and 417.
LCM(414,417) = 21×32×231×1391
LCM(414,417) = 57546
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 417
List of positive integer factors of 417 that divides 417 without a remainder.
1, 3, 139, 417
Least Common Multiple of 414 and 417 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 417, than apply into the LCM equation.
GCF(414,417) = 3
LCM(414,417) = ( 414 × 417) / 3
LCM(414,417) = 172638 / 3
LCM(414,417) = 57546
Properties of LCM 414 and 417
(i) The LCM of 417 and 414 is associative
LCM of 414 and 417 = LCM of 417 and 414
Related Least Common Multiples of 414
Related Least Common Multiples of 417
Frequently Asked Questions on LCM of 414 and 417
1. What is the LCM of 414 and 417?
Answer: LCM of 414 and 417 is 57546.
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 417?
Answer: Factors of 417 are 1, 3, 139, 417. There are 4 integers that are factors of 417. The greatest factor of 417 is 417.
4. How to Find the LCM of 414 and 417?
Answer:
Least Common Multiple of 414 and 417 = 57546
Step 1: Find the prime factorization of 414
414 = 2 x 3 x 3 x 23
Step 2: Find the prime factorization of 417
417 = 3 x 139
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 57546 = 2 x 3 x 3 x 23 x 139
Step 4: Therefore, the least common multiple of 414 and 417 is 57546.