Least Common Multiple of 31409 and 31414
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 31409 and 31414 the smallest integer that is 986682326 that is divisible by both numbers.
Least Common Multiple (LCM) of 31409 and 31414 is 986682326.
LCM(31409,31414) = 986682326
LCM of 31409 and 31414
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 31409 and 31414 by Prime method
- Least Common Multiple of 31409 and 31414 with GCF Formula
LCM of 31409 and 31414 is 986682326
Least common multiple can be found by multiplying the highest exponent prime factors of 31409 and 31414. First we will calculate the prime factors of 31409 and 31414.
Prime Factorization of 31409
| 7 | 31409 |
| 7 | 4487 |
| 641 | 641 |
| 1 |
Prime factors of 31409 are 7,641. Prime factorization of 31409 in exponential form is:
31409 = 72×6411
Prime Factorization of 31414
| 2 | 31414 |
| 113 | 15707 |
| 139 | 139 |
| 1 |
Prime factors of 31414 are 2, 113,139. Prime factorization of 31414 in exponential form is:
31414 = 21×1131×1391
Now multiplying the highest exponent prime factors to calculate the LCM of 31409 and 31414.
LCM(31409,31414) = 21×72×1131×1391×6411
LCM(31409,31414) = 986682326
Factors of 31409
List of positive integer factors of 31409 that divides 31409 without a remainder.
1, 7, 49, 641, 4487, 31409
Factors of 31414
List of positive integer factors of 31414 that divides 31414 without a remainder.
1, 2, 113, 139, 226, 278, 15707, 31414
Least Common Multiple of 31409 and 31414 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31409 and 31414, than apply into the LCM equation.
GCF(31409,31414) = 1
LCM(31409,31414) = ( 31409 × 31414) / 1
LCM(31409,31414) = 986682326 / 1
LCM(31409,31414) = 986682326
Properties of LCM 31409 and 31414
(i) The LCM of 31414 and 31409 is associative
LCM of 31409 and 31414 = LCM of 31414 and 31409
Related Least Common Multiples of 31409
Related Least Common Multiples of 31414
Frequently Asked Questions on LCM of 31409 and 31414
1. What is the LCM of 31409 and 31414?
Answer: LCM of 31409 and 31414 is 986682326.
2. What are the Factors of 31409?
Answer: Factors of 31409 are 1, 7, 49, 641, 4487, 31409. There are 6 integers that are factors of 31409. The greatest factor of 31409 is 31409.
3. What are the Factors of 31414?
Answer: Factors of 31414 are 1, 2, 113, 139, 226, 278, 15707, 31414. There are 8 integers that are factors of 31414. The greatest factor of 31414 is 31414.
4. How to Find the LCM of 31409 and 31414?
Answer:
Least Common Multiple of 31409 and 31414 = 986682326
Step 1: Find the prime factorization of 31409
31409 = 7 x 7 x 641
Step 2: Find the prime factorization of 31414
31414 = 2 x 113 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 = 986682326 = 2 x 7 x 7 x 113 x 139 x 641
Step 4: Therefore, the least common multiple of 31409 and 31414 is 986682326.