Question

Find the HCF and LCM of 496 and 1116.

Answer 1

Answer:

here is the answer

hope it helps you

Step-by-step explanation:

Since , 1116 > 496

We apply the division lemma to 1116 and 496

1116 = 496 × 2 + 124

Since the remainder 496 ≠ 0 , we apply division lemma to 496 and 124

496 = 124 × 3 + 0

The reminder now become zero so our procedure stops

Since , the divisor at this stage is 124

the HCF of 1116 and 496 is 124

LCM=>

The instructions to find the LCM of 496 and 1116 are the next:

1. Decompose all numbers into prime factors

496 2 248 2 124 2 62 2 31 31 1  1116 2 558 2 279 3 93 3 31 31 1  

2. Write all numbers as the product of its prime factors

Prime factors of 496 = 24 . 31

Prime factors of 1116 = 22 . 32 . 31

3. Choose the common and uncommon prime factors with the greatest exponent

Common prime factors: 2 , 31

Common prime factors with the greatest exponent: 24, 311

Uncommon prime factors: 3

Uncommon prime factors with the greatest exponent: 32

4. Calculate the Least Common Multiple or LCM

Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

LCM = 24. 311. 32 = 4464

Answer 2

Answer:

The HCF and LCM of 496 and 1116 are 124 and 4464 respectively.

Highest Common Factor:

• The highest common factor (HCF) or greatest common divisor (GCD) is the largest number that divides each of the given numbers.
• Example: The HCF of 6 (3×2) and 18 (3×3×2) is 6 as both are divisible by 6 and no other number greater than 6 can divide both of them.

Least Common Multiple:

• The least common multiple or LCM is the smallest multiple of all the given numbers.
• In other terms, the LCM is the smallest integer that is divisible by all the numbers.
• The formula to find LCM is $lcm(a,b) = \frac{ab}{gcd(a,b)}$.
• Example: The LCM of 6 and 18 is $\frac{6*18}{gcd(6,18)} = \frac{108}{6}=18$

Step-by-step explanation:

Step 1: To find the HCF

To find HCF, we divide the largest among the two numbers by the other number. Since, 1116 > 496, we divide 1116 by 496.

Division of 1116 by 496 gives the quotient as 2 and the remainder as 124.

1116 / 496 = 496 × 2 + 124

Since the remainder is not zero, we divide 496 by 124.

496 / 124 = 124 × 4 + 0

The division of 496 by 124 gives the remainder as zero.

Therefore, 124 is the HCF of 496 and 1116.

Step 2: To find the LCM

We know that $lcm(a,b) = \frac{ab}{gcd(a,b)}$

Substituting the values, we get

$LCM(496, 1116) = \frac{496 * 1116}{GCD(496, 1116)}$

$LCM(496, 1116) = \frac{5553536}{124}$

$LCM(496, 1116) = 4464$

Therefore, 4464 is the LCM of 496 and 1116.

Hence, 124 is the HCF, and 1116 is the LCM of 496 and 1116.

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