Least Common Multiple (LCM) of 118 and 33
The least common multiple (LCM) of 118 and 33 is 3894.
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 118 and 33?
First, calculate the GCD of 118 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 33 = 3 remainder 19 |
| 2 | 33 ÷ 19 = 1 remainder 14 |
| 3 | 19 ÷ 14 = 1 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 109 | 1308 |
| 108 and 141 | 5076 |
| 114 and 36 | 684 |
| 149 and 19 | 2831 |
| 24 and 114 | 456 |