Least Common Multiple (LCM) of 114 and 162
The least common multiple (LCM) of 114 and 162 is 3078.
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 162?
First, calculate the GCD of 114 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 162 = 0 remainder 114 |
| 2 | 162 ÷ 114 = 1 remainder 48 |
| 3 | 114 ÷ 48 = 2 remainder 18 |
| 4 | 48 ÷ 18 = 2 remainder 12 |
| 5 | 18 ÷ 12 = 1 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 99 | 16731 |
| 49 and 105 | 735 |
| 47 and 194 | 9118 |
| 73 and 64 | 4672 |
| 110 and 117 | 12870 |