Least Common Multiple (LCM) of 66 and 119
The least common multiple (LCM) of 66 and 119 is 7854.
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 66 and 119?
First, calculate the GCD of 66 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 119 = 0 remainder 66 |
| 2 | 119 ÷ 66 = 1 remainder 53 |
| 3 | 66 ÷ 53 = 1 remainder 13 |
| 4 | 53 ÷ 13 = 4 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 38 | 2204 |
| 41 and 51 | 2091 |
| 132 and 162 | 3564 |
| 124 and 154 | 9548 |
| 76 and 71 | 5396 |