Least Common Multiple (LCM) of 119 and 33
The least common multiple (LCM) of 119 and 33 is 3927.
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 119 and 33?
First, calculate the GCD of 119 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 33 = 3 remainder 20 |
| 2 | 33 ÷ 20 = 1 remainder 13 |
| 3 | 20 ÷ 13 = 1 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 71 | 2911 |
| 140 and 140 | 140 |
| 80 and 56 | 560 |
| 99 and 111 | 3663 |
| 110 and 115 | 2530 |