Least Common Multiple of 1406 and 1413
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1406 and 1413 the smallest integer that is 1986678 that is divisible by both numbers.
Least Common Multiple (LCM) of 1406 and 1413 is 1986678.
LCM(1406,1413) = 1986678
LCM of 1406 and 1413
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 1406 and 1413 by Prime method
- Least Common Multiple of 1406 and 1413 with GCF Formula
LCM of 1406 and 1413 is 1986678
Least common multiple can be found by multiplying the highest exponent prime factors of 1406 and 1413. First we will calculate the prime factors of 1406 and 1413.
Prime Factorization of 1406
| 2 | 1406 |
| 19 | 703 |
| 37 | 37 |
| 1 |
Prime factors of 1406 are 2, 19,37. Prime factorization of 1406 in exponential form is:
1406 = 21×191×371
Prime Factorization of 1413
| 3 | 1413 |
| 3 | 471 |
| 157 | 157 |
| 1 |
Prime factors of 1413 are 3,157. Prime factorization of 1413 in exponential form is:
1413 = 32×1571
Now multiplying the highest exponent prime factors to calculate the LCM of 1406 and 1413.
LCM(1406,1413) = 21×32×191×371×1571
LCM(1406,1413) = 1986678
Factors of 1406
List of positive integer factors of 1406 that divides 1406 without a remainder.
1, 2, 19, 37, 38, 74, 703, 1406
Factors of 1413
List of positive integer factors of 1413 that divides 1413 without a remainder.
1, 3, 9, 157, 471, 1413
Least Common Multiple of 1406 and 1413 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1406 and 1413, than apply into the LCM equation.
GCF(1406,1413) = 1
LCM(1406,1413) = ( 1406 × 1413) / 1
LCM(1406,1413) = 1986678 / 1
LCM(1406,1413) = 1986678
Properties of LCM 1406 and 1413
(i) The LCM of 1413 and 1406 is associative
LCM of 1406 and 1413 = LCM of 1413 and 1406
Related Least Common Multiples of 1406
Related Least Common Multiples of 1413
Frequently Asked Questions on LCM of 1406 and 1413
1. What is the LCM of 1406 and 1413?
Answer: LCM of 1406 and 1413 is 1986678.
2. What are the Factors of 1406?
Answer: Factors of 1406 are 1, 2, 19, 37, 38, 74, 703, 1406. There are 8 integers that are factors of 1406. The greatest factor of 1406 is 1406.
3. What are the Factors of 1413?
Answer: Factors of 1413 are 1, 3, 9, 157, 471, 1413. There are 6 integers that are factors of 1413. The greatest factor of 1413 is 1413.
4. How to Find the LCM of 1406 and 1413?
Answer:
Least Common Multiple of 1406 and 1413 = 1986678
Step 1: Find the prime factorization of 1406
1406 = 2 x 19 x 37
Step 2: Find the prime factorization of 1413
1413 = 3 x 3 x 157
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1986678 = 2 x 3 x 3 x 19 x 37 x 157
Step 4: Therefore, the least common multiple of 1406 and 1413 is 1986678.