Least Common Multiple (LCM) of 114 and 119
The least common multiple (LCM) of 114 and 119 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 114 and 119?
First, calculate the GCD of 114 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 119 = 0 remainder 114 |
| 2 | 119 ÷ 114 = 1 remainder 5 |
| 3 | 114 ÷ 5 = 22 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 55 | 6435 |
| 36 and 139 | 5004 |
| 102 and 145 | 14790 |
| 80 and 75 | 1200 |
| 176 and 101 | 17776 |