Question

find the LCM &HCF of the following numbers 30&72 &432
​

Answer 1

$\bf \huge \red{Answer}$

Applying Euclid's division lemma to 30 and 72

Since 72>30

72=30×2+12 ....... (1)

30=12×2+6 ...... (2)

12=6×2+0 ...... (3)

The remainder has now become zero,

Since the divisor at this stage is 6

The HCF of 30 and 72 is 6

Now from (2), we have

30=12×2+6

Rearrange this

6=30−12×2

⇒6=30−[(72−30×2)×2] { from ( 1 ) }

⇒6=30−72×2+4×30 [ using distributive property ]

⇒6=30×(5)+72×(−2) ...... (4)

According to the problem,

d=30x+72y ........ (5)

Comparing (4) and (5), we get

x=5 and y=−2

$\bf \huge \blue{Happy learning}$