Least Common Multiple (LCM) of 137 and 35
The least common multiple (LCM) of 137 and 35 is 4795.
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 137 and 35?
First, calculate the GCD of 137 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 35 = 3 remainder 32 |
| 2 | 35 ÷ 32 = 1 remainder 3 |
| 3 | 32 ÷ 3 = 10 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 186 | 4836 |
| 69 and 169 | 11661 |
| 155 and 70 | 2170 |
| 86 and 184 | 7912 |
| 104 and 159 | 16536 |