Least Common Multiple (LCM) of 21 and 78
The least common multiple (LCM) of 21 and 78 is 546.
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 78?
First, calculate the GCD of 21 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 78 = 0 remainder 21 |
| 2 | 78 ÷ 21 = 3 remainder 15 |
| 3 | 21 ÷ 15 = 1 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 88 | 8184 |
| 14 and 158 | 1106 |
| 135 and 62 | 8370 |
| 143 and 25 | 3575 |
| 64 and 111 | 7104 |