Least Common Multiple (LCM) of 119 and 114
The least common multiple (LCM) of 119 and 114 is 13566.
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 114?
First, calculate the GCD of 119 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 114 = 1 remainder 5 |
| 2 | 114 ÷ 5 = 22 remainder 4 |
| 3 | 5 ÷ 4 = 1 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 106 | 5406 |
| 154 and 63 | 1386 |
| 33 and 97 | 3201 |
| 99 and 90 | 990 |
| 59 and 31 | 1829 |