Least Common Multiple (LCM) of 21 and 154
The least common multiple (LCM) of 21 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 21 and 154?
First, calculate the GCD of 21 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 154 = 0 remainder 21 |
| 2 | 154 ÷ 21 = 7 remainder 7 |
| 3 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 35 | 5985 |
| 125 and 14 | 1750 |
| 142 and 60 | 4260 |
| 124 and 120 | 3720 |
| 197 and 83 | 16351 |