Least Common Multiple (LCM) of 42 and 154
The least common multiple (LCM) of 42 and 154 is 462.
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 42 and 154?
First, calculate the GCD of 42 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 154 = 0 remainder 42 |
| 2 | 154 ÷ 42 = 3 remainder 28 |
| 3 | 42 ÷ 28 = 1 remainder 14 |
| 4 | 28 ÷ 14 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 143 | 15301 |
| 44 and 153 | 6732 |
| 178 and 115 | 20470 |
| 121 and 199 | 24079 |
| 16 and 96 | 96 |