Least Common Multiple (LCM) of 116 and 147
The least common multiple (LCM) of 116 and 147 is 17052.
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 147?
First, calculate the GCD of 116 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 147 = 0 remainder 116 |
| 2 | 147 ÷ 116 = 1 remainder 31 |
| 3 | 116 ÷ 31 = 3 remainder 23 |
| 4 | 31 ÷ 23 = 1 remainder 8 |
| 5 | 23 ÷ 8 = 2 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 49 | 7056 |
| 170 and 117 | 19890 |
| 80 and 20 | 80 |
| 142 and 169 | 23998 |
| 145 and 184 | 26680 |