Least Common Multiple (LCM) of 169 and 98
The least common multiple (LCM) of 169 and 98 is 16562.
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 169 and 98?
First, calculate the GCD of 169 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 98 = 1 remainder 71 |
| 2 | 98 ÷ 71 = 1 remainder 27 |
| 3 | 71 ÷ 27 = 2 remainder 17 |
| 4 | 27 ÷ 17 = 1 remainder 10 |
| 5 | 17 ÷ 10 = 1 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 154 | 770 |
| 197 and 157 | 30929 |
| 178 and 75 | 13350 |
| 117 and 182 | 1638 |
| 153 and 138 | 7038 |