Least Common Multiple (LCM) of 27 and 119
The least common multiple (LCM) of 27 and 119 is 3213.
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 27 and 119?
First, calculate the GCD of 27 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 119 = 0 remainder 27 |
| 2 | 119 ÷ 27 = 4 remainder 11 |
| 3 | 27 ÷ 11 = 2 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 178 | 6942 |
| 192 and 97 | 18624 |
| 161 and 107 | 17227 |
| 129 and 86 | 258 |
| 80 and 153 | 12240 |