Least Common Multiple (LCM) of 51 and 98
The least common multiple (LCM) of 51 and 98 is 4998.
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 51 and 98?
First, calculate the GCD of 51 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 98 = 0 remainder 51 |
| 2 | 98 ÷ 51 = 1 remainder 47 |
| 3 | 51 ÷ 47 = 1 remainder 4 |
| 4 | 47 ÷ 4 = 11 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 71 | 10366 |
| 118 and 107 | 12626 |
| 160 and 156 | 6240 |
| 197 and 91 | 17927 |
| 112 and 105 | 1680 |