Least Common Multiple of 1407 and 1414
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1407 and 1414 the smallest integer that is 284214 that is divisible by both numbers.
Least Common Multiple (LCM) of 1407 and 1414 is 284214.
LCM(1407,1414) = 284214
LCM of 1407 and 1414
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 1407 and 1414 by Prime method
- Least Common Multiple of 1407 and 1414 with GCF Formula
LCM of 1407 and 1414 is 284214
Least common multiple can be found by multiplying the highest exponent prime factors of 1407 and 1414. First we will calculate the prime factors of 1407 and 1414.
Prime Factorization of 1407
| 3 | 1407 |
| 7 | 469 |
| 67 | 67 |
| 1 |
Prime factors of 1407 are 3, 7,67. Prime factorization of 1407 in exponential form is:
1407 = 31×71×671
Prime Factorization of 1414
| 2 | 1414 |
| 7 | 707 |
| 101 | 101 |
| 1 |
Prime factors of 1414 are 2, 7,101. Prime factorization of 1414 in exponential form is:
1414 = 21×71×1011
Now multiplying the highest exponent prime factors to calculate the LCM of 1407 and 1414.
LCM(1407,1414) = 21×31×71×671×1011
LCM(1407,1414) = 284214
Factors of 1407
List of positive integer factors of 1407 that divides 1407 without a remainder.
1, 3, 7, 21, 67, 201, 469, 1407
Factors of 1414
List of positive integer factors of 1414 that divides 1414 without a remainder.
1, 2, 7, 14, 101, 202, 707, 1414
Least Common Multiple of 1407 and 1414 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1407 and 1414, than apply into the LCM equation.
GCF(1407,1414) = 7
LCM(1407,1414) = ( 1407 × 1414) / 7
LCM(1407,1414) = 1989498 / 7
LCM(1407,1414) = 284214
Properties of LCM 1407 and 1414
(i) The LCM of 1414 and 1407 is associative
LCM of 1407 and 1414 = LCM of 1414 and 1407
Related Least Common Multiples of 1407
Related Least Common Multiples of 1414
Frequently Asked Questions on LCM of 1407 and 1414
1. What is the LCM of 1407 and 1414?
Answer: LCM of 1407 and 1414 is 284214.
2. What are the Factors of 1407?
Answer: Factors of 1407 are 1, 3, 7, 21, 67, 201, 469, 1407. There are 8 integers that are factors of 1407. The greatest factor of 1407 is 1407.
3. What are the Factors of 1414?
Answer: Factors of 1414 are 1, 2, 7, 14, 101, 202, 707, 1414. There are 8 integers that are factors of 1414. The greatest factor of 1414 is 1414.
4. How to Find the LCM of 1407 and 1414?
Answer:
Least Common Multiple of 1407 and 1414 = 284214
Step 1: Find the prime factorization of 1407
1407 = 3 x 7 x 67
Step 2: Find the prime factorization of 1414
1414 = 2 x 7 x 101
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 284214 = 2 x 3 x 7 x 67 x 101
Step 4: Therefore, the least common multiple of 1407 and 1414 is 284214.