Least Common Multiple (LCM) of 116 and 151
The least common multiple (LCM) of 116 and 151 is 17516.
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 151?
First, calculate the GCD of 116 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 151 = 0 remainder 116 |
| 2 | 151 ÷ 116 = 1 remainder 35 |
| 3 | 116 ÷ 35 = 3 remainder 11 |
| 4 | 35 ÷ 11 = 3 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 128 | 1920 |
| 50 and 179 | 8950 |
| 52 and 172 | 2236 |
| 105 and 50 | 1050 |
| 174 and 25 | 4350 |