Least Common Multiple (LCM) of 167 and 116
The least common multiple (LCM) of 167 and 116 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 167 and 116?
First, calculate the GCD of 167 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 116 = 1 remainder 51 |
| 2 | 116 ÷ 51 = 2 remainder 14 |
| 3 | 51 ÷ 14 = 3 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 179 | 3043 |
| 36 and 47 | 1692 |
| 104 and 81 | 8424 |
| 37 and 188 | 6956 |
| 93 and 133 | 12369 |