Least Common Multiple (LCM) of 36 and 93
The least common multiple (LCM) of 36 and 93 is 1116.
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 93?
First, calculate the GCD of 36 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 93 = 0 remainder 36 |
| 2 | 93 ÷ 36 = 2 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 |
|---|---|
| 130 and 135 | 3510 |
| 107 and 143 | 15301 |
| 199 and 121 | 24079 |
| 180 and 17 | 3060 |
| 22 and 139 | 3058 |