Least Common Multiple (LCM) of 116 and 167
The least common multiple (LCM) of 116 and 167 is 19372.
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 167?
First, calculate the GCD of 116 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 167 = 0 remainder 116 |
| 2 | 167 ÷ 116 = 1 remainder 51 |
| 3 | 116 ÷ 51 = 2 remainder 14 |
| 4 | 51 ÷ 14 = 3 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 178 | 2670 |
| 104 and 99 | 10296 |
| 170 and 108 | 9180 |
| 171 and 93 | 5301 |
| 107 and 106 | 11342 |