Least Common Multiple (LCM) of 61 and 120
The least common multiple (LCM) of 61 and 120 is 7320.
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 61 and 120?
First, calculate the GCD of 61 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 120 = 0 remainder 61 |
| 2 | 120 ÷ 61 = 1 remainder 59 |
| 3 | 61 ÷ 59 = 1 remainder 2 |
| 4 | 59 ÷ 2 = 29 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 43 | 1806 |
| 21 and 78 | 546 |
| 23 and 170 | 3910 |
| 142 and 143 | 20306 |
| 103 and 138 | 14214 |