Least Common Multiple of 450 and 455
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 450 and 455 the smallest integer that is 40950 that is divisible by both numbers.
Least Common Multiple (LCM) of 450 and 455 is 40950.
LCM(450,455) = 40950
LCM of 450 and 455
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 450 and 455 by Prime method
- Least Common Multiple of 450 and 455 with GCF Formula
LCM of 450 and 455 is 40950
Least common multiple can be found by multiplying the highest exponent prime factors of 450 and 455. First we will calculate the prime factors of 450 and 455.
Prime Factorization of 450
| 2 | 450 |
| 3 | 225 |
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 450 are 2, 3,5. Prime factorization of 450 in exponential form is:
450 = 21×32×52
Prime Factorization of 455
| 5 | 455 |
| 7 | 91 |
| 13 | 13 |
| 1 |
Prime factors of 455 are 5, 7,13. Prime factorization of 455 in exponential form is:
455 = 51×71×131
Now multiplying the highest exponent prime factors to calculate the LCM of 450 and 455.
LCM(450,455) = 21×32×52×71×131
LCM(450,455) = 40950
Factors of 450
List of positive integer factors of 450 that divides 450 without a remainder.
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Factors of 455
List of positive integer factors of 455 that divides 455 without a remainder.
1, 5, 7, 13, 35, 65, 91, 455
Least Common Multiple of 450 and 455 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 450 and 455, than apply into the LCM equation.
GCF(450,455) = 5
LCM(450,455) = ( 450 × 455) / 5
LCM(450,455) = 204750 / 5
LCM(450,455) = 40950
Properties of LCM 450 and 455
(i) The LCM of 455 and 450 is associative
LCM of 450 and 455 = LCM of 455 and 450
Related Least Common Multiples of 450
Related Least Common Multiples of 455
Frequently Asked Questions on LCM of 450 and 455
1. What is the LCM of 450 and 455?
Answer: LCM of 450 and 455 is 40950.
2. What are the Factors of 450?
Answer: Factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450. There are 18 integers that are factors of 450. The greatest factor of 450 is 450.
3. What are the Factors of 455?
Answer: Factors of 455 are 1, 5, 7, 13, 35, 65, 91, 455. There are 8 integers that are factors of 455. The greatest factor of 455 is 455.
4. How to Find the LCM of 450 and 455?
Answer:
Least Common Multiple of 450 and 455 = 40950
Step 1: Find the prime factorization of 450
450 = 2 x 3 x 3 x 5 x 5
Step 2: Find the prime factorization of 455
455 = 5 x 7 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 40950 = 2 x 3 x 3 x 5 x 5 x 7 x 13
Step 4: Therefore, the least common multiple of 450 and 455 is 40950.