Least Common Multiple (LCM) of 167 and 36
The least common multiple (LCM) of 167 and 36 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 167 and 36?
First, calculate the GCD of 167 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 36 = 4 remainder 23 |
| 2 | 36 ÷ 23 = 1 remainder 13 |
| 3 | 23 ÷ 13 = 1 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 89 | 5963 |
| 108 and 79 | 8532 |
| 66 and 90 | 990 |
| 68 and 49 | 3332 |
| 30 and 126 | 630 |