LCM of 40 and 50 is the the smallest number among all usual multiples that 40 and 50. The first few multiples the 40 and 50 are (40, 80, 120, 160, 200, 240, 280, . . . ) and (50, 100, 150, 200, 250, 300, . . . ) respectively. There room 3 typically used methods to uncover LCM the 40 and also 50 - by element factorization, by division method, and by listing multiples.

You are watching: What is the least common multiple of 40 and 50

1. | LCM that 40 and 50 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** LCM of 40 and also 50 is 200.

**Explanation: **

The LCM of two non-zero integers, x(40) and also y(50), is the smallest hopeful integer m(200) the is divisible through both x(40) and y(50) without any kind of remainder.

Let's look at the different methods for finding the LCM of 40 and also 50.

By prime Factorization MethodBy Listing MultiplesBy division Method### LCM of 40 and 50 by prime Factorization

Prime administrate of 40 and 50 is (2 × 2 × 2 × 5) = 23 × 51 and also (2 × 5 × 5) = 21 × 52 respectively. LCM of 40 and 50 deserve to be obtained by multiply prime determinants raised to their respective highest possible power, i.e. 23 × 52 = 200.Hence, the LCM of 40 and 50 by prime factorization is 200.

### LCM the 40 and 50 by Listing Multiples

To calculation the LCM the 40 and also 50 by listing the end the common multiples, we can follow the given below steps:

**Step 1:**perform a few multiples of 40 (40, 80, 120, 160, 200, 240, 280, . . . ) and 50 (50, 100, 150, 200, 250, 300, . . . . )

**Step 2:**The usual multiples indigenous the multiples of 40 and 50 space 200, 400, . . .

**Step 3:**The smallest common multiple that 40 and 50 is 200.

∴ The least usual multiple the 40 and 50 = 200.

### LCM that 40 and also 50 by department Method

To calculate the LCM that 40 and also 50 through the department method, we will divide the numbers(40, 50) by your prime components (preferably common). The product of this divisors gives the LCM the 40 and 50.

**Step 3:**proceed the measures until just 1s space left in the critical row.

The LCM the 40 and also 50 is the product of every prime number on the left, i.e. LCM(40, 50) by department method = 2 × 2 × 2 × 5 × 5 = 200.

**☛ likewise Check:**

**Example 2: Verify the relationship between GCF and LCM that 40 and 50. **

**Solution: **

The relation in between GCF and LCM of 40 and also 50 is provided as,LCM(40, 50) × GCF(40, 50) = Product that 40, 50Prime administrate of 40 and 50 is given as, 40 = (2 × 2 × 2 × 5) = 23 × 51 and also 50 = (2 × 5 × 5) = 21 × 52LCM(40, 50) = 200GCF(40, 50) = 10LHS = LCM(40, 50) × GCF(40, 50) = 200 × 10 = 2000RHS = Product that 40, 50 = 40 × 50 = 2000⇒ LHS = RHS = 2000Hence, verified.

## FAQs top top LCM the 40 and 50

### What is the LCM of 40 and also 50?

The **LCM the 40 and 50 is 200**. To discover the least common multiple the 40 and 50, we need to discover the multiples that 40 and also 50 (multiples of 40 = 40, 80, 120, 160 . . . . 200; multiples of 50 = 50, 100, 150, 200) and choose the the smallest multiple the is exactly divisible through 40 and also 50, i.e., 200.

### How to find the LCM of 40 and also 50 by element Factorization?

To discover the LCM that 40 and also 50 using prime factorization, us will uncover the element factors, (40 = 2 × 2 × 2 × 5) and (50 = 2 × 5 × 5). LCM of 40 and also 50 is the product the prime determinants raised to your respective highest possible exponent among the numbers 40 and 50.⇒ LCM the 40, 50 = 23 × 52 = 200.

### What is the the very least Perfect Square Divisible by 40 and also 50?

The least number divisible through 40 and also 50 = LCM(40, 50)LCM of 40 and 50 = 2 × 2 × 2 × 5 × 5

### Which of the following is the LCM that 40 and also 50? 10, 200, 40, 36

The value of LCM that 40, 50 is the smallest common multiple that 40 and also 50. The number to solve the given problem is 200.

### If the LCM the 50 and also 40 is 200, find its GCF.

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LCM(50, 40) × GCF(50, 40) = 50 × 40Since the LCM of 50 and 40 = 200⇒ 200 × GCF(50, 40) = 2000Therefore, the greatest usual factor (GCF) = 2000/200 = 10.