Question

Find the LCM and HCF of 17, 23,and 29 by applying the Prime factorisation method.
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Answer 1

Answer:

Step-by-step explanation:

LCM by applying the Prime factorisation method.

Let us find the HCF of 17,23,29

17 = 17 × 1

23 = 23 × 1

29 = 29 × 1

∴ HCF (17,23,29) = 1

Let us find the LCM of17,23,29

LCM(17,23,29) = 17 × 23 × 29

∴ LCM(17,23,29) = 11339

Let us verify LCM and HCF is equals to the product of three numbers

LCM × HCF =17 × 23 × 29

17 × 23 × 29 × 1 =17 × 23 × 29

11339 = 11339

HCF by applying the Prime factorisation method

HCF of 17, 23 and 29 can be represented as HCF of (HCF of 17, 23) and 29. HCF(17, 23, 29) can be thus calculated by first finding HCF (17, 23) using long division and thereafter using this result with 29 to perform long division again.

Step 1: Divide 23 (larger number) by 17 (smaller number).

Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (17) by the remainder (6). Repeat this process until the remainder = 0.

⇒ HCF(17, 23) = 1.

Step 3: Now to find the HCF of 1 and 29, we will perform a long division on 29 and 1.

Step 4: For remainder = 0, divisor = 1 ⇒ HCF(1, 29) = 1

Thus, HCF(17, 23, 29) = HCF(HCF(17, 23), 29) = 1.