Least Common Multiple (LCM) of 63 and 84
The least common multiple (LCM) of 63 and 84 is 252.
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 63 and 84?
First, calculate the GCD of 63 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 84 = 0 remainder 63 |
| 2 | 84 ÷ 63 = 1 remainder 21 |
| 3 | 63 ÷ 21 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 165 | 4290 |
| 179 and 144 | 25776 |
| 100 and 35 | 700 |
| 188 and 43 | 8084 |
| 190 and 72 | 6840 |