Least Common Multiple (LCM) of 21 and 77
The least common multiple (LCM) of 21 and 77 is 231.
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 77?
First, calculate the GCD of 21 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 77 = 0 remainder 21 |
| 2 | 77 ÷ 21 = 3 remainder 14 |
| 3 | 21 ÷ 14 = 1 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 106 | 8056 |
| 154 and 133 | 2926 |
| 90 and 75 | 450 |
| 10 and 82 | 410 |
| 159 and 164 | 26076 |