Least Common Multiple (LCM) of 53 and 59
The least common multiple (LCM) of 53 and 59 is 3127.
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 59?
First, calculate the GCD of 53 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 59 = 0 remainder 53 |
| 2 | 59 ÷ 53 = 1 remainder 6 |
| 3 | 53 ÷ 6 = 8 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 68 | 3604 |
| 102 and 150 | 2550 |
| 65 and 54 | 3510 |
| 129 and 17 | 2193 |
| 143 and 70 | 10010 |