Least Common Multiple (LCM) of 61 and 78
The least common multiple (LCM) of 61 and 78 is 4758.
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 78?
First, calculate the GCD of 61 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 78 = 0 remainder 61 |
| 2 | 78 ÷ 61 = 1 remainder 17 |
| 3 | 61 ÷ 17 = 3 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 157 | 18055 |
| 118 and 20 | 1180 |
| 191 and 10 | 1910 |
| 160 and 141 | 22560 |
| 103 and 81 | 8343 |