Least Common Multiple (LCM) of 114 and 151
The least common multiple (LCM) of 114 and 151 is 17214.
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 151?
First, calculate the GCD of 114 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 151 = 0 remainder 114 |
| 2 | 151 ÷ 114 = 1 remainder 37 |
| 3 | 114 ÷ 37 = 3 remainder 3 |
| 4 | 37 ÷ 3 = 12 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 90 | 450 |
| 10 and 70 | 70 |
| 10 and 33 | 330 |
| 104 and 39 | 312 |
| 142 and 150 | 10650 |