Least Common Multiple (LCM) of 84 and 35
The least common multiple (LCM) of 84 and 35 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 84 and 35?
First, calculate the GCD of 84 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 35 = 2 remainder 14 |
| 2 | 35 ÷ 14 = 2 remainder 7 |
| 3 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 183 | 10980 |
| 111 and 29 | 3219 |
| 24 and 33 | 264 |
| 32 and 96 | 96 |
| 115 and 163 | 18745 |