Least Common Multiple (LCM) of 105 and 84
The least common multiple (LCM) of 105 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 105 and 84?
First, calculate the GCD of 105 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 84 = 1 remainder 21 |
| 2 | 84 ÷ 21 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 53 | 8533 |
| 152 and 65 | 9880 |
| 144 and 80 | 720 |
| 178 and 89 | 178 |
| 194 and 80 | 7760 |