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Lcd Of 7 And 8

LCM of 7 and 8

LCM of seven and viii is the smallest number among all mutual multiples of 7 and 8. The first few multiples of vii and 8 are (7, 14, 21, 28, . . . ) and (viii, sixteen, 24, 32, 40, 48, 56, . . . ) respectively. There are iii commonly used methods to find LCM of vii and 8 - by listing multiples, by prime factorization, and by partition method.

ane. LCM of 7 and 8
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of seven and 8?

Answer: LCM of 7 and 8 is 56.

LCM of 7 and 8

Explanation:

The LCM of two non-zero integers, x(7) and y(8), is the smallest positive integer m(56) that is divisible by both x(7) and y(viii) without whatever rest.

Methods to Find LCM of 7 and eight

Let's look at the dissimilar methods for finding the LCM of seven and 8.

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

LCM of vii and 8 by Prime Factorization

Prime factorization of 7 and viii is (7) = 71 and (2 × ii × two) = twothree respectively. LCM of 7 and eight can be obtained by multiplying prime number factors raised to their respective highest power, i.e. 23 × 7i = 56.
Hence, the LCM of 7 and 8 by prime factorization is 56.

LCM of 7 and 8 by Division Method

LCM of 7 and 8 by Division Method

To calculate the LCM of 7 and 8 by the segmentation method, nosotros will split up the numbers(7, 8) by their prime factors (preferably common). The production of these divisors gives the LCM of 7 and 8.

  • Stride 1: Observe the smallest prime number that is a factor of at least one of the numbers, vii and 8. Write this prime(two) on the left of the given numbers(7 and 8), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (7, viii) is a multiple of 2, divide it by 2 and write the caliber beneath it. Bring down whatever number that is non divisible by the prime.
  • Step iii: Continue the steps until only 1s are left in the terminal row.

The LCM of seven and eight is the product of all prime number numbers on the left, i.e. LCM(vii, 8) past segmentation method = ii × two × ii × 7 = 56.

LCM of 7 and 8 by Listing Multiples

LCM of 7 and 8 by Listing Multiples Method

To calculate the LCM of 7 and 8 by list out the common multiples, we can follow the given beneath steps:

  • Step 1: Listing a few multiples of 7 (7, 14, 21, 28, . . . ) and 8 (viii, xvi, 24, 32, forty, 48, 56, . . . . )
  • Step 2: The common multiples from the multiples of seven and 8 are 56, 112, . . .
  • Step three: The smallest common multiple of 7 and 8 is 56.

∴ The least common multiple of vii and 8 = 56.

☛ Also Cheque:

  • LCM of ten and 12 - 60
  • LCM of 18 and 45 - ninety
  • LCM of 20, 25 and 30 - 300
  • LCM of 30 and 35 - 210
  • LCM of 28 and xxx - 420
  • LCM of 3, 4 and 7 - 84
  • LCM of 7 and 11 - 77

FAQs on LCM of 7 and 8

What is the LCM of 7 and 8?

The LCM of 7 and 8 is 56 . To find the LCM of seven and 8, we need to find the multiples of seven and 8 (multiples of 7 = seven, 14, 21, 28 . . . . 56; multiples of viii = 8, 16, 24, 32 . . . . 56) and choose the smallest multiple that is exactly divisible by vii and 8, i.due east., 56.

What is the Least Perfect Foursquare Divisible by vii and 8?

The least number divisible by 7 and viii = LCM(7, 8)
LCM of seven and 8 = two × two × 2 × seven [Incomplete pair(s): 2, seven]
⇒ Least perfect square divisible past each 7 and 8 = LCM(7, eight) × two × 7 = 784 [Square root of 784 = √784 = ±28]
Therefore, 784 is the required number.

What is the Relation Between GCF and LCM of vii, viii?

The following equation can exist used to express the relation between GCF and LCM of 7 and 8, i.east. GCF × LCM = vii × 8.

If the LCM of eight and 7 is 56, Find its GCF.

LCM(eight, vii) × GCF(viii, seven) = 8 × vii
Since the LCM of 8 and 7 = 56
⇒ 56 × GCF(8, vii) = 56
Therefore, the GCF (greatest common factor) = 56/56 = ane.

How to Detect the LCM of 7 and 8 by Prime Factorization?

To find the LCM of vii and 8 using prime factorization, we will find the prime number factors, (7 = 7) and (eight = 2 × two × 2). LCM of 7 and 8 is the production of prime factors raised to their respective highest exponent among the numbers 7 and 8.
⇒ LCM of seven, 8 = 2three × vii1 = 56.

Lcd Of 7 And 8,

Source: https://www.cuemath.com/numbers/lcm-of-7-and-8/

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