krit.club logo

Prime Time - Common Multiples and Common Factors

Grade 6CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

A factor of a number is an exact divisor of that number. For example, the factors of 1212 are 1,2,3,4,6,1, 2, 3, 4, 6, and 1212.

•

Common Factors are factors that are shared by two or more numbers. For 1212 and 1818, the common factors are 1,2,3,1, 2, 3, and 66.

•

The Highest Common Factor (HCFHCF) is the greatest among the common factors of two or more numbers. It is also known as the Greatest Common Divisor (GCDGCD).

•

Multiples of a number are obtained by multiplying the number by 1,2,3,…1, 2, 3, \dots. For example, multiples of 55 are 5,10,15,20,…5, 10, 15, 20, \dots.

•

Common Multiples are multiples shared by two or more numbers. For 44 and 66, common multiples include 12,24,36,…12, 24, 36, \dots.

•

The Least Common Multiple (LCMLCM) is the smallest of the common multiples of two or more numbers.

•

Two numbers are called co-prime if their only common factor is 11. For example, 88 and 1515 are co-prime because HCF(8,15)=1HCF(8, 15) = 1.

📐Formulae

Product of two numbers=HCF×LCMProduct\ of\ two\ numbers = HCF \times LCM

HCF=Number1×Number2LCMHCF = \frac{Number_1 \times Number_2}{LCM}

LCM=Number1×Number2HCFLCM = \frac{Number_1 \times Number_2}{HCF}

💡Examples

Problem 1:

Find the HCFHCF of 2424 and 3636 using the listing factors method.

Solution:

Factors of 24:1,2,3,4,6,8,12,2424: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36:1,2,3,4,6,9,12,18,3636: 1, 2, 3, 4, 6, 9, 12, 18, 36 Common Factors: 1,2,3,4,6,121, 2, 3, 4, 6, 12 HCF=12HCF = 12

Explanation:

We list all divisors for both numbers and identify the largest number present in both lists.

Problem 2:

Find the LCMLCM of 1212 and 1515.

Solution:

Multiples of 12:12,24,36,48,60,72,…12: 12, 24, 36, 48, 60, 72, \dots Multiples of 15:15,30,45,60,75,…15: 15, 30, 45, 60, 75, \dots Common Multiples: 60,120,…60, 120, \dots LCM=60LCM = 60

Explanation:

The LCMLCM is the smallest number that is a multiple of both 1212 and 1515.

Problem 3:

The HCFHCF of two numbers is 66 and their LCMLCM is 3636. If one number is 1212, find the other number using the relationship formula.

Solution:

Let the other number be xx. Using the formula Product=HCF×LCMProduct = HCF \times LCM: 12×x=6×3612 \times x = 6 \times 36 12x=21612x = 216 x=21612x = \frac{216}{12} x=18x = 18 Verification of the product calculation: 36×6216\begin{array}{r} 36 \\ \times 6 \\ \hline 216 \end{array}

Explanation:

We use the mathematical property that the product of HCFHCF and LCMLCM of two numbers is equal to the product of the numbers themselves.