What is the G.C.F and L.C.M of 36 and 45?

The Greatest Common Factor (G.C.F) and the Least Common Multiple (L.C.M) are important concepts in mathematics, especially when dealing with numbers like 36 and 45.

Finding the G.C.F

The G.C.F is the largest number that divides both numbers without leaving a remainder. To find the G.C.F of 36 and 45, we can list the factors:

• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• Factors of 45: 1, 3, 5, 9, 15, 45

The common factors are 1, 3, and 9. Thus, the G.C.F is 9.

Calculating the L.C.M

The L.C.M is the smallest number that both 36 and 45 can divide into without a remainder. One way to find the L.C.M is to use the relationship between G.C.F and L.C.M:

L.C.M = (Product of the numbers) / G.C.F

So, we calculate:

• Product of 36 and 45: 36 × 45 = 1620
• L.C.M = 1620 / 9 = 180

Therefore, the L.C.M of 36 and 45 is 180.

Summary

In summary, for the numbers 36 and 45:

• G.C.F: 9
• L.C.M: 180