Least Common Multiple (LCM) of 154 and 112
The least common multiple (LCM) of 154 and 112 is 1232.
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 112?
First, calculate the GCD of 154 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 112 = 1 remainder 42 |
| 2 | 112 ÷ 42 = 2 remainder 28 |
| 3 | 42 ÷ 28 = 1 remainder 14 |
| 4 | 28 ÷ 14 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 156 | 8580 |
| 137 and 71 | 9727 |
| 54 and 114 | 1026 |
| 55 and 68 | 3740 |
| 166 and 98 | 8134 |