Least Common Multiple of 420 and 423
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 423 the smallest integer that is 59220 that is divisible by both numbers.
Least Common Multiple (LCM) of 420 and 423 is 59220.
LCM(420,423) = 59220
LCM of 420 and 423
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 420 and 423 by Prime method
- Least Common Multiple of 420 and 423 with GCF Formula
LCM of 420 and 423 is 59220
Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 423. First we will calculate the prime factors of 420 and 423.
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 423
| 3 | 423 |
| 3 | 141 |
| 47 | 47 |
| 1 |
Prime factors of 423 are 3,47. Prime factorization of 423 in exponential form is:
423 = 32×471
Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 423.
LCM(420,423) = 22×32×51×71×471
LCM(420,423) = 59220
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 423
List of positive integer factors of 423 that divides 423 without a remainder.
1, 3, 9, 47, 141, 423
Least Common Multiple of 420 and 423 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 423, than apply into the LCM equation.
GCF(420,423) = 3
LCM(420,423) = ( 420 × 423) / 3
LCM(420,423) = 177660 / 3
LCM(420,423) = 59220
Properties of LCM 420 and 423
(i) The LCM of 423 and 420 is associative
LCM of 420 and 423 = LCM of 423 and 420
Related Least Common Multiples of 420
Related Least Common Multiples of 423
Frequently Asked Questions on LCM of 420 and 423
1. What is the LCM of 420 and 423?
Answer: LCM of 420 and 423 is 59220.
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 423?
Answer: Factors of 423 are 1, 3, 9, 47, 141, 423. There are 6 integers that are factors of 423. The greatest factor of 423 is 423.
4. How to Find the LCM of 420 and 423?
Answer:
Least Common Multiple of 420 and 423 = 59220
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 423
423 = 3 x 3 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 59220 = 2 x 2 x 3 x 3 x 5 x 7 x 47
Step 4: Therefore, the least common multiple of 420 and 423 is 59220.