Least Common Multiple (LCM) of 35 and 169
The least common multiple (LCM) of 35 and 169 is 5915.
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 35 and 169?
First, calculate the GCD of 35 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 169 = 0 remainder 35 |
| 2 | 169 ÷ 35 = 4 remainder 29 |
| 3 | 35 ÷ 29 = 1 remainder 6 |
| 4 | 29 ÷ 6 = 4 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 184 | 16008 |
| 198 and 118 | 11682 |
| 80 and 62 | 2480 |
| 163 and 31 | 5053 |
| 184 and 111 | 20424 |