Least Common Multiple (LCM) of 84 and 49
The least common multiple (LCM) of 84 and 49 is 588.
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 49?
First, calculate the GCD of 84 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 49 = 1 remainder 35 |
| 2 | 49 ÷ 35 = 1 remainder 14 |
| 3 | 35 ÷ 14 = 2 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 176 | 1760 |
| 109 and 61 | 6649 |
| 115 and 139 | 15985 |
| 177 and 194 | 34338 |
| 112 and 194 | 10864 |