Least Common Multiple (LCM) of 60 and 84
The least common multiple (LCM) of 60 and 84 is 420.
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 60 and 84?
First, calculate the GCD of 60 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 84 = 0 remainder 60 |
| 2 | 84 ÷ 60 = 1 remainder 24 |
| 3 | 60 ÷ 24 = 2 remainder 12 |
| 4 | 24 ÷ 12 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 15 | 60 |
| 105 and 19 | 1995 |
| 185 and 181 | 33485 |
| 26 and 193 | 5018 |
| 80 and 92 | 1840 |