Least Common Multiple (LCM) of 116 and 72
The least common multiple (LCM) of 116 and 72 is 2088.
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 116 and 72?
First, calculate the GCD of 116 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 72 = 1 remainder 44 |
| 2 | 72 ÷ 44 = 1 remainder 28 |
| 3 | 44 ÷ 28 = 1 remainder 16 |
| 4 | 28 ÷ 16 = 1 remainder 12 |
| 5 | 16 ÷ 12 = 1 remainder 4 |
| 6 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 154 | 6160 |
| 95 and 83 | 7885 |
| 51 and 92 | 4692 |
| 70 and 42 | 210 |
| 74 and 33 | 2442 |