Least Common Multiple of 420 and 427
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 420 and 427 the smallest integer that is 25620 that is divisible by both numbers.
Least Common Multiple (LCM) of 420 and 427 is 25620.
LCM(420,427) = 25620
LCM of 420 and 427
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 420 and 427 by Prime method
- Least Common Multiple of 420 and 427 with GCF Formula
LCM of 420 and 427 is 25620
Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 427. First we will calculate the prime factors of 420 and 427.
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
Prime Factorization of 427
| 7 | 427 |
| 61 | 61 |
| 1 |
Prime factors of 427 are 7,61. Prime factorization of 427 in exponential form is:
427 = 71×611
Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 427.
LCM(420,427) = 22×31×51×71×611
LCM(420,427) = 25620
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
Factors of 427
List of positive integer factors of 427 that divides 427 without a remainder.
1, 7, 61, 427
Least Common Multiple of 420 and 427 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 420 and 427, than apply into the LCM equation.
GCF(420,427) = 7
LCM(420,427) = ( 420 × 427) / 7
LCM(420,427) = 179340 / 7
LCM(420,427) = 25620
Properties of LCM 420 and 427
(i) The LCM of 427 and 420 is associative
LCM of 420 and 427 = LCM of 427 and 420
Related Least Common Multiples of 420
Related Least Common Multiples of 427
Frequently Asked Questions on LCM of 420 and 427
1. What is the LCM of 420 and 427?
Answer: LCM of 420 and 427 is 25620.
2. 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.
3. What are the Factors of 427?
Answer: Factors of 427 are 1, 7, 61, 427. There are 4 integers that are factors of 427. The greatest factor of 427 is 427.
4. How to Find the LCM of 420 and 427?
Answer:
Least Common Multiple of 420 and 427 = 25620
Step 1: Find the prime factorization of 420
420 = 2 x 2 x 3 x 5 x 7
Step 2: Find the prime factorization of 427
427 = 7 x 61
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 25620 = 2 x 2 x 3 x 5 x 7 x 61
Step 4: Therefore, the least common multiple of 420 and 427 is 25620.