Least Common Multiple (LCM) of 59 and 98
The least common multiple (LCM) of 59 and 98 is 5782.
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 59 and 98?
First, calculate the GCD of 59 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 98 = 0 remainder 59 |
| 2 | 98 ÷ 59 = 1 remainder 39 |
| 3 | 59 ÷ 39 = 1 remainder 20 |
| 4 | 39 ÷ 20 = 1 remainder 19 |
| 5 | 20 ÷ 19 = 1 remainder 1 |
| 6 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 119 | 12019 |
| 49 and 46 | 2254 |
| 181 and 157 | 28417 |
| 169 and 52 | 676 |
| 133 and 94 | 12502 |