Least Common Multiple (LCM) of 45 and 114
The least common multiple (LCM) of 45 and 114 is 1710.
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 45 and 114?
First, calculate the GCD of 45 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 114 = 0 remainder 45 |
| 2 | 114 ÷ 45 = 2 remainder 24 |
| 3 | 45 ÷ 24 = 1 remainder 21 |
| 4 | 24 ÷ 21 = 1 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 16 | 1936 |
| 149 and 109 | 16241 |
| 154 and 78 | 6006 |
| 159 and 94 | 14946 |
| 93 and 41 | 3813 |