Question

FInd the HCF and LCM of any three numbers of using colour buttons or colour papers sripes are colour ribbons

Answer 1

Hi there!

♦ Aim :-

To find the HCF of two numbers experimentally based on Euclid's division lemma.

♦ Material Required :-

Square sheet and maths kit.

♦ Procedure ( Ye can perform this activity yourself ) :-

i.

Cut one strip of length “a” units (a = 11 cm) and one strip of length “b” units (b = 8 cm) of width 1 cm each (a > b).

ii.

Paste the strips of length “a” units above the strip of length “b” units aligning them from length as shown in fig 1. The remaining length is say c cm (c = 3 cm, b > c).

iii.

Cut another strip of length b units and 2 strips of c units. Paste the strip of b units above the strips of c unit aligning them from left ad shown in fig 2. The remaining length is say d cm. (d = 2 cm, d < c)

iv.

Repeat the process till the length proceeding strips covered completely and second strip which covers the proceeding strips is the HCF of given number. fig 4

♦ Observation

By Euclid's division lemma a = bq + r, 0 ≤ r < b

→ Fig 1. Shows a = b × 1 + c (q = 1,r = c)

→ Fig 2. shows b = c × 2 + d (q = 2,r = d)

→ Fig 3. shows c = d × 1 + e (q = 1, r = e)

→ Fig 4. shows d = e × 2 + 0 (q = 2, r = 0)

H.C.F. of a and b is e.

Here, a = 11 cm, b = 8 cm, c = 3 cm, d = 2 cm and e = 1 cm

H.C.F of 11 and 8 is 1.

♦ Conclusion:-

Euclid's division lemma can be used for finding the HCF of two or more numbers.

Hope it helps! :)

Answer 2

Answer:

H.C.F of any three number can be determined by taking prime factorization of each number and find out the common number in each number. Hence the common factor calculated.

LCM of any three number can be determined by taking prime factorization of each number and find out the least common factor from each number and multiply it and get the L.C.M.