Question

the HCF of two numbers is 5 and 30 respectively. if one of the number is 10, find the other number​

Answer 1

$\huge\mathfrak{Answer:}$

$\large\underline{\sf{\blue{Correct \: Question:}}}$

The HCF and LCM of two numbers is 5 and 30 respectively. If one of the number is 10, find the other number

$\large\underline{\sf{\blue{Given:}}}$

• We have been that HCF and LCM of two numbers is 5 and 30 respectively
• One number is 10

$\large\underline{\sf{\blue{To \: Find :}}}$

• We have to find the other number

$\large\underline{\sf{\blue{Solution:}}}$

Let the other number be = x

• HCF of numbers = 5
• LCM of numbers = 30

$\large\underline{\mathfrak\red{We \: know \: that :}}$

$\mapsto \boxed{\sf{HCF \times LCM = Product \: of \: Numbers}}$

$\mapsto \sf{5 \times 30 = x \times 10}$

$\mapsto \sf{10x = 150}$

$\mapsto \sf{x = \dfrac{150}{10}}$

$\mapsto \boxed{\sf{x = 15}}$

$\sf{}$

Hence the other Number is 15

___________________________

$\large\purple{\underline{\underline{\mathtt{Extra \: Information:}}}}$

• Least Common Multiple
• Least common multiple usually known as LCM of two numbers a and b is the smallest positive integer that is divisible by both a and b
• For Eg : 6 is LCM of 2 and 3

• Highest Common Factor
• The greatest common divisor of two or more integers which is a non zero is called its HCF
• For Eg : HCF of 8 and 12 is 4

___________________________

Answer 2

Given :  hcf and lcm of two numbers is 5 and 30 respectively

one of the number is 10

To Find :   the other number

Solution:

Product of LCM and HCF of two numbers = Product of the two numbers

HCF( a, b)  = 5

LCM (a , b) = 30

a = 10

b = ?

a * b = HCF( a, b)   * LCM( a, b)  

=> 10 * b  = 5 * 30

=> b = 15

Hence other numbers is 15

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