Least Common Multiple (LCM) of 154 and 106
The least common multiple (LCM) of 154 and 106 is 8162.
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 154 and 106?
First, calculate the GCD of 154 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 106 = 1 remainder 48 |
| 2 | 106 ÷ 48 = 2 remainder 10 |
| 3 | 48 ÷ 10 = 4 remainder 8 |
| 4 | 10 ÷ 8 = 1 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 117 | 13572 |
| 59 and 68 | 4012 |
| 107 and 95 | 10165 |
| 78 and 122 | 4758 |
| 91 and 189 | 2457 |