Least Common Multiple (LCM) of 167 and 98
The least common multiple (LCM) of 167 and 98 is 16366.
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 167 and 98?
First, calculate the GCD of 167 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 98 = 1 remainder 69 |
| 2 | 98 ÷ 69 = 1 remainder 29 |
| 3 | 69 ÷ 29 = 2 remainder 11 |
| 4 | 29 ÷ 11 = 2 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 155 | 3720 |
| 158 and 90 | 7110 |
| 153 and 107 | 16371 |
| 112 and 87 | 9744 |
| 40 and 95 | 760 |