Least Common Multiple (LCM) of 105 and 36
The least common multiple (LCM) of 105 and 36 is 1260.
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 105 and 36?
First, calculate the GCD of 105 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 36 = 2 remainder 33 |
| 2 | 36 ÷ 33 = 1 remainder 3 |
| 3 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 170 | 33490 |
| 46 and 88 | 2024 |
| 62 and 144 | 4464 |
| 148 and 56 | 2072 |
| 193 and 118 | 22774 |