Least Common Multiple (LCM) of 21 and 196
The least common multiple (LCM) of 21 and 196 is 588.
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 196?
First, calculate the GCD of 21 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 196 = 0 remainder 21 |
| 2 | 196 ÷ 21 = 9 remainder 7 |
| 3 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 165 | 13695 |
| 198 and 142 | 14058 |
| 120 and 92 | 2760 |
| 200 and 153 | 30600 |
| 47 and 45 | 2115 |