Least Common Multiple (LCM) of 36 and 98
The least common multiple (LCM) of 36 and 98 is 1764.
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 36 and 98?
First, calculate the GCD of 36 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 98 = 0 remainder 36 |
| 2 | 98 ÷ 36 = 2 remainder 26 |
| 3 | 36 ÷ 26 = 1 remainder 10 |
| 4 | 26 ÷ 10 = 2 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 78 | 5304 |
| 141 and 131 | 18471 |
| 88 and 85 | 7480 |
| 105 and 192 | 6720 |
| 116 and 18 | 1044 |