Least Common Multiple of 413 and 420
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 413 and 420 the smallest integer that is 24780 that is divisible by both numbers.
Least Common Multiple (LCM) of 413 and 420 is 24780.
LCM(413,420) = 24780
LCM of 413 and 420
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 413 and 420 by Prime method
- Least Common Multiple of 413 and 420 with GCF Formula
LCM of 413 and 420 is 24780
Least common multiple can be found by multiplying the highest exponent prime factors of 413 and 420. First we will calculate the prime factors of 413 and 420.
Prime Factorization of 413
| 7 | 413 |
| 59 | 59 |
| 1 |
Prime factors of 413 are 7,59. Prime factorization of 413 in exponential form is:
413 = 71×591
Prime Factorization of 420
| 2 | 420 |
| 2 | 210 |
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 420 are 2, 3, 5,7. Prime factorization of 420 in exponential form is:
420 = 22×31×51×71
Now multiplying the highest exponent prime factors to calculate the LCM of 413 and 420.
LCM(413,420) = 22×31×51×71×591
LCM(413,420) = 24780
Factors of 413
List of positive integer factors of 413 that divides 413 without a remainder.
1, 7, 59, 413
Factors of 420
List of positive integer factors of 420 that divides 420 without a remainder.
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
Least Common Multiple of 413 and 420 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 413 and 420, than apply into the LCM equation.
GCF(413,420) = 7
LCM(413,420) = ( 413 × 420) / 7
LCM(413,420) = 173460 / 7
LCM(413,420) = 24780
Properties of LCM 413 and 420
(i) The LCM of 420 and 413 is associative
LCM of 413 and 420 = LCM of 420 and 413
Related Least Common Multiples of 413
Related Least Common Multiples of 420
Frequently Asked Questions on LCM of 413 and 420
1. What is the LCM of 413 and 420?
Answer: LCM of 413 and 420 is 24780.
2. What are the Factors of 413?
Answer: Factors of 413 are 1, 7, 59, 413. There are 4 integers that are factors of 413. The greatest factor of 413 is 413.
3. What are the Factors of 420?
Answer: Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. There are 24 integers that are factors of 420. The greatest factor of 420 is 420.
4. How to Find the LCM of 413 and 420?
Answer:
Least Common Multiple of 413 and 420 = 24780
Step 1: Find the prime factorization of 413
413 = 7 x 59
Step 2: Find the prime factorization of 420
420 = 2 x 2 x 3 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 24780 = 2 x 2 x 3 x 5 x 7 x 59
Step 4: Therefore, the least common multiple of 413 and 420 is 24780.