Least Common Multiple (LCM) of 105 and 114
The least common multiple (LCM) of 105 and 114 is 3990.
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 105 and 114?
First, calculate the GCD of 105 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 114 = 0 remainder 105 |
| 2 | 114 ÷ 105 = 1 remainder 9 |
| 3 | 105 ÷ 9 = 11 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 182 | 13286 |
| 140 and 72 | 2520 |
| 151 and 12 | 1812 |
| 65 and 171 | 11115 |
| 93 and 183 | 5673 |