Least Common Multiple (LCM) of 36 and 61
The least common multiple (LCM) of 36 and 61 is 2196.
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 61?
First, calculate the GCD of 36 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 61 = 0 remainder 36 |
| 2 | 61 ÷ 36 = 1 remainder 25 |
| 3 | 36 ÷ 25 = 1 remainder 11 |
| 4 | 25 ÷ 11 = 2 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 112 | 10640 |
| 27 and 138 | 1242 |
| 66 and 50 | 1650 |
| 132 and 105 | 4620 |
| 99 and 165 | 495 |