Least Common Multiple (LCM) of 61 and 96
The least common multiple (LCM) of 61 and 96 is 5856.
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 96?
First, calculate the GCD of 61 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 96 = 0 remainder 61 |
| 2 | 96 ÷ 61 = 1 remainder 35 |
| 3 | 61 ÷ 35 = 1 remainder 26 |
| 4 | 35 ÷ 26 = 1 remainder 9 |
| 5 | 26 ÷ 9 = 2 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 89 | 8544 |
| 80 and 113 | 9040 |
| 142 and 80 | 5680 |
| 130 and 28 | 1820 |
| 113 and 121 | 13673 |