Lcm Of 6 12 15

LCM of 6, 12, and 15

LCM of half-dozen, 12, and 15 is the smallest number among all common multiples of half dozen, 12, and fifteen. The first few multiples of 6, 12, and fifteen are (half dozen, 12, 18, 24, thirty . . .), (12, 24, 36, 48, 60 . . .), and (15, 30, 45, lx, 75 . . .) respectively. At that place are 3 unremarkably used methods to find LCM of 6, 12, 15 - by listing multiples, by segmentation method, and by prime factorization.

one.	LCM of half dozen, 12, and fifteen
two.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of six, 12, and 15?

Answer: LCM of half-dozen, 12, and 15 is 60.

Explanation:

The LCM of three non-cypher integers, a(6), b(12), and c(fifteen), is the smallest positive integer m(60) that is divisible by a(half-dozen), b(12), and c(15) without any remainder.

Methods to Find LCM of 6, 12, and 15

Permit'south look at the different methods for finding the LCM of half-dozen, 12, and fifteen.

• By Division Method
• Past Prime Factorization Method
• By Listing Multiples

LCM of 6, 12, and xv by Partitioning Method

To calculate the LCM of vi, 12, and 15 by the sectionalization method, we will divide the numbers(half-dozen, 12, 15) by their prime number factors (preferably common). The product of these divisors gives the LCM of half-dozen, 12, and 15.

• Step 1: Discover the smallest prime number that is a factor of at least 1 of the numbers, 6, 12, and 15. Write this prime number(ii) on the left of the given numbers(six, 12, and fifteen), separated every bit per the ladder organization.
• Step two: If any of the given numbers (6, 12, 15) is a multiple of 2, divide it by 2 and write the quotient below it. Bring downwardly whatsoever number that is not divisible by the prime number number.
• Step 3: Continue the steps until simply 1s are left in the last row.

The LCM of 6, 12, and 15 is the product of all prime numbers on the left, i.due east. LCM(half-dozen, 12, 15) by partition method = 2 × 2 × 3 × 5 = 60.

LCM of half-dozen, 12, and xv by Prime number Factorization

Prime number factorization of 6, 12, and 15 is (2 × three) = 2¹ × 3¹, (2 × 2 × 3) = 2² × 3¹, and (3 × 5) = 3¹ × 5¹ respectively. LCM of 6, 12, and fifteen can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^two × 3¹ × 5¹ = 60.
Hence, the LCM of 6, 12, and 15 past prime factorization is threescore.

LCM of half dozen, 12, and 15 by Listing Multiples

To summate the LCM of vi, 12, 15 by listing out the mutual multiples, nosotros tin follow the given beneath steps:

• Stride 1: List a few multiples of vi (half-dozen, 12, 18, 24, xxx . . .), 12 (12, 24, 36, 48, 60 . . .), and 15 (15, 30, 45, threescore, 75 . . .).
• Step 2: The common multiples from the multiples of 6, 12, and 15 are 60, 120, . . .
• Footstep three: The smallest common multiple of 6, 12, and 15 is 60.

∴ The least common multiple of 6, 12, and 15 = 60.

☛ Too Check:

• LCM of 80, 85 and 90 - 12240
• LCM of 20 and 24 - 120
• LCM of 50 and 70 - 350
• LCM of 36, 48 and 54 - 432
• LCM of four and 16 - xvi
• LCM of 16 and 22 - 176
• LCM of 45 and 99 - 495

FAQs on LCM of half dozen, 12, and 15

What is the LCM of half-dozen, 12, and 15?

The LCM of 6, 12, and 15 is 60 . To find the least common multiple of 6, 12, and 15, we need to find the multiples of 6, 12, and xv (multiples of 6 = 6, 12, 18, 24 . . . . lx . . . . ; multiples of 12 = 12, 24, 36, 48 . . . . 60 . . . . ; multiples of 15 = fifteen, 30, 45, 60 . . . .) and choose the smallest multiple that is exactly divisible past six, 12, and 15, i.e., lx.

What is the Least Perfect Square Divisible past 6, 12, and xv?

The least number divisible by half dozen, 12, and 15 = LCM(6, 12, xv)
LCM of 6, 12, and fifteen = 2 × 2 × 3 × 5 [Incomplete pair(due south): 3, 5]
⇒ Least perfect square divisible by each six, 12, and 15 = LCM(6, 12, fifteen) × iii × 5 = 900 [Foursquare root of 900 = √900 = ±thirty]
Therefore, 900 is the required number.

How to Detect the LCM of vi, 12, and fifteen by Prime Factorization?

To detect the LCM of 6, 12, and fifteen using prime factorization, we volition notice the prime factors, (half dozen = 2¹ × threeⁱ), (12 = 2² × three¹), and (fifteen = three¹ × v^ane). LCM of 6, 12, and fifteen is the product of prime factors raised to their respective highest exponent among the numbers vi, 12, and 15.
⇒ LCM of 6, 12, 15 = 2² × 3¹ × 5ⁱ = 60.

Which of the following is the LCM of 6, 12, and 15? xviii, sixty, 28, 11

The value of LCM of six, 12, 15 is the smallest mutual multiple of 6, 12, and fifteen. The number satisfying the given condition is 60.

Lcm Of 6 12 15,

Source: https://www.cuemath.com/numbers/lcm-of-6-12-and-15/

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