Least Common Multiple (LCM) of 114 and 61
The least common multiple (LCM) of 114 and 61 is 6954.
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 114 and 61?
First, calculate the GCD of 114 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 61 = 1 remainder 53 |
| 2 | 61 ÷ 53 = 1 remainder 8 |
| 3 | 53 ÷ 8 = 6 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 44 | 1408 |
| 93 and 142 | 13206 |
| 33 and 41 | 1353 |
| 178 and 18 | 1602 |
| 165 and 13 | 2145 |