LCM of 3, 4, and also 5 is the smallest number amongst all usual multiples that 3, 4, and 5. The first couple of multiples of 3, 4, and also 5 space (3, 6, 9, 12, 15 . . .), (4, 8, 12, 16, 20 . . .), and also (5, 10, 15, 20, 25 . . .) respectively. There space 3 generally used methods to uncover LCM the 3, 4, 5 - by listing multiples, by department method, and by prime factorization.

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1.LCM the 3, 4, and also 5
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM that 3, 4, and also 5 is 60.

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Explanation:

The LCM of 3 non-zero integers, a(3), b(4), and c(5), is the smallest optimistic integer m(60) the is divisible by a(3), b(4), and c(5) without any kind of remainder.


Let's look at the different methods for finding the LCM of 3, 4, and 5.

By element Factorization MethodBy division MethodBy Listing Multiples

LCM that 3, 4, and also 5 by element Factorization

Prime administrate of 3, 4, and also 5 is (3) = 31, (2 × 2) = 22, and (5) = 51 respectively. LCM that 3, 4, and also 5 deserve to be acquired by multiply prime determinants raised to your respective greatest power, i.e. 22 × 31 × 51 = 60.Hence, the LCM the 3, 4, and 5 by prime factorization is 60.

LCM that 3, 4, and also 5 by division Method

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To calculation the LCM of 3, 4, and 5 by the department method, we will divide the numbers(3, 4, 5) by your prime components (preferably common). The product of these divisors gives the LCM that 3, 4, and also 5.

Step 2: If any of the offered numbers (3, 4, 5) is a lot of of 2, divide it through 2 and also write the quotient listed below it. Carry down any type of number the is not divisible by the prime number.Step 3: proceed the steps until just 1s space left in the critical row.

The LCM the 3, 4, and 5 is the product of every prime number on the left, i.e. LCM(3, 4, 5) by division method = 2 × 2 × 3 × 5 = 60.

LCM that 3, 4, and 5 by Listing Multiples

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To calculate the LCM of 3, 4, 5 by listing out the common multiples, we can follow the given listed below steps:

Step 1: perform a few multiples the 3 (3, 6, 9, 12, 15 . . .), 4 (4, 8, 12, 16, 20 . . .), and also 5 (5, 10, 15, 20, 25 . . .).Step 2: The common multiples from the multiples that 3, 4, and 5 space 60, 120, . . .Step 3: The smallest typical multiple the 3, 4, and 5 is 60.

∴ The least common multiple that 3, 4, and 5 = 60.

☛ additionally Check:


Example 2: discover the the smallest number that is divisible through 3, 4, 5 exactly.

Solution:

The worth of LCM(3, 4, 5) will be the smallest number the is exactly divisible through 3, 4, and 5.⇒ Multiples that 3, 4, and also 5:

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 48, 51, 54, 57, 60, . . . .Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 52, 56, 60, . . . .Multiples the 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 45, 50, 55, 60, . . . .

Therefore, the LCM of 3, 4, and 5 is 60.


Example 3: Verify the relationship between the GCD and also LCM of 3, 4, and also 5.

Solution:

The relation in between GCD and also LCM the 3, 4, and also 5 is offered as,LCM(3, 4, 5) = <(3 × 4 × 5) × GCD(3, 4, 5)>/⇒ prime factorization the 3, 4 and also 5:

3 = 314 = 225 = 51

∴ GCD of (3, 4), (4, 5), (3, 5) and also (3, 4, 5) = 1, 1, 1 and also 1 respectively.Now, LHS = LCM(3, 4, 5) = 60.And, RHS = <(3 × 4 × 5) × GCD(3, 4, 5)>/ = <(60) × 1>/<1 × 1 × 1> = 60LHS = RHS = 60.Hence verified.


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FAQs on LCM the 3, 4, and 5

What is the LCM the 3, 4, and 5?

The LCM of 3, 4, and 5 is 60. To discover the least common multiple that 3, 4, and 5, we need to find the multiples that 3, 4, and 5 (multiples the 3 = 3, 6, 9, 12 . . . . 60 . . . . ; multiples that 4 = 4, 8, 12, 16 . . . . 60 . . . . ; multiples of 5 = 5, 10, 15, 20 . . . . 60 . . . . ) and also choose the the smallest multiple the is exactly divisible through 3, 4, and 5, i.e., 60.

What is the Relation in between GCF and also LCM the 3, 4, 5?

The adhering to equation can be offered to express the relation in between GCF and also LCM the 3, 4, 5, i.e. LCM(3, 4, 5) = <(3 × 4 × 5) × GCF(3, 4, 5)>/.

How to discover the LCM of 3, 4, and also 5 by element Factorization?

To find the LCM that 3, 4, and 5 making use of prime factorization, we will uncover the element factors, (3 = 31), (4 = 22), and (5 = 51). LCM of 3, 4, and 5 is the product that prime determinants raised to their respective greatest exponent among the number 3, 4, and also 5.⇒ LCM the 3, 4, 5 = 22 × 31 × 51 = 60.

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Which that the following is the LCM that 3, 4, and also 5? 28, 20, 5, 60

The worth of LCM the 3, 4, 5 is the smallest typical multiple of 3, 4, and also 5. The number to solve the given condition is 60.