Least Common Multiple (LCM) of 60 and 91
The least common multiple (LCM) of 60 and 91 is 5460.
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 60 and 91?
First, calculate the GCD of 60 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 91 = 0 remainder 60 |
| 2 | 91 ÷ 60 = 1 remainder 31 |
| 3 | 60 ÷ 31 = 1 remainder 29 |
| 4 | 31 ÷ 29 = 1 remainder 2 |
| 5 | 29 ÷ 2 = 14 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 135 | 13905 |
| 68 and 82 | 2788 |
| 164 and 93 | 15252 |
| 44 and 119 | 5236 |
| 63 and 156 | 3276 |