Least Common Multiple (LCM) of 36 and 167
The least common multiple (LCM) of 36 and 167 is 6012.
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 36 and 167?
First, calculate the GCD of 36 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 167 = 0 remainder 36 |
| 2 | 167 ÷ 36 = 4 remainder 23 |
| 3 | 36 ÷ 23 = 1 remainder 13 |
| 4 | 23 ÷ 13 = 1 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 135 | 1350 |
| 150 and 181 | 27150 |
| 182 and 195 | 2730 |
| 42 and 26 | 546 |
| 120 and 82 | 4920 |