Least Common Multiple (LCM) of 53 and 135
The least common multiple (LCM) of 53 and 135 is 7155.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 53 and 135?
First, calculate the GCD of 53 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 135 = 0 remainder 53 |
| 2 | 135 ÷ 53 = 2 remainder 29 |
| 3 | 53 ÷ 29 = 1 remainder 24 |
| 4 | 29 ÷ 24 = 1 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 88 | 8360 |
| 99 and 93 | 3069 |
| 140 and 37 | 5180 |
| 13 and 111 | 1443 |
| 119 and 12 | 1428 |