Least Common Multiple (LCM) of 167 and 196
The least common multiple (LCM) of 167 and 196 is 32732.
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 196?
First, calculate the GCD of 167 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 196 = 0 remainder 167 |
| 2 | 196 ÷ 167 = 1 remainder 29 |
| 3 | 167 ÷ 29 = 5 remainder 22 |
| 4 | 29 ÷ 22 = 1 remainder 7 |
| 5 | 22 ÷ 7 = 3 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 32 | 3680 |
| 141 and 156 | 7332 |
| 138 and 65 | 8970 |
| 24 and 85 | 2040 |
| 190 and 10 | 190 |