Least Common Multiple (LCM) of 36 and 165
The least common multiple (LCM) of 36 and 165 is 1980.
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 165?
First, calculate the GCD of 36 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 165 = 0 remainder 36 |
| 2 | 165 ÷ 36 = 4 remainder 21 |
| 3 | 36 ÷ 21 = 1 remainder 15 |
| 4 | 21 ÷ 15 = 1 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 69 | 1173 |
| 22 and 73 | 1606 |
| 110 and 60 | 660 |
| 63 and 157 | 9891 |
| 133 and 48 | 6384 |