Least Common Multiple (LCM) of 45 and 84
The least common multiple (LCM) of 45 and 84 is 1260.
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 45 and 84?
First, calculate the GCD of 45 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 84 = 0 remainder 45 |
| 2 | 84 ÷ 45 = 1 remainder 39 |
| 3 | 45 ÷ 39 = 1 remainder 6 |
| 4 | 39 ÷ 6 = 6 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 142 | 3692 |
| 60 and 82 | 2460 |
| 199 and 149 | 29651 |
| 23 and 171 | 3933 |
| 33 and 160 | 5280 |