Least Common Multiple (LCM) of 36 and 59
The least common multiple (LCM) of 36 and 59 is 2124.
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 36 and 59?
First, calculate the GCD of 36 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 59 = 0 remainder 36 |
| 2 | 59 ÷ 36 = 1 remainder 23 |
| 3 | 36 ÷ 23 = 1 remainder 13 |
| 4 | 23 ÷ 13 = 1 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 102 | 3570 |
| 45 and 138 | 2070 |
| 172 and 76 | 3268 |
| 153 and 177 | 9027 |
| 62 and 124 | 124 |