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# HCF & LCM Maths Study Materials | Quantitative Aptitude

**Factors and Multiples**

- If number
*a*divided another number*b*exactly, we say that*a*is a**factor**of*b*. - In this case,
*b*is called a**multiple**of*a*.

**H.C.F. & L.C.M.**

**Factorization & Division Method****HCF & LCM of Fractions & Decimal Fractions**

**Highest Common Factor (H.C.F.) or Greatest Common Measure (G.C.M.) or Greatest Common Divisor (G.C.D.)**

**Factorization Method**

Write each number as the product of the prime factors. The product of least powers of common prime factors gives H.C.F.

**Example:**

**Find the H.C.F. of 108, 288 and 360.**

**108 = 2 ^{2}✘3^{3}, 288 = 2^{5}✘32 and 360 = 23✘5✘32**

**H.C.F. = 22✘32=36**

**
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**Division Method**

Let we have two numbers .Pick the smaller one and divide it by the larger one. After that divide the divisor with the remainder. This process of dividing the preceding number by the remainder will repeated until we got the zero as remainder.The last divisor is the required H.C.F.

**Example:**

**H.C.F. & L.C.M. of Fractions**

**H.C.F. = ^{H.C.F. of Numerator }/_{ L.C.M. of Denominators}**

**Product of H.C.F. & L.C.M.**

**H.C.F * L.C.M. = product of two numbers**

**Decimal numbers**

H.C.F. of Decimal numbers

**Step 1**. Find the HCF of the given numbers without decimal.

**Step 2.**Put the decimal point ( in the HCF of Step 1) from right to left ccording to the MAXIMUM decimal places among the given numbers.

**Least Common Multiple (L.C.M.):**

**Factorization Method**

Write each numbers into a product of prime factors. Then, L.C.M is the product of highest powers of all the factors.

**Examples:**

**Find the L.C.M. of 72, 108 and 2100.**

** 72=23✘32,108=33✘22,**

** 2100=22✘52✘3✘7.**

** L.C.M.=23✘33✘52✘7=37800**

**Division Method**

- Let we have set of numbers.
- First of all find the number which divide at least two of the number in a given set of number.remainder and

not divisible numbers will carry forward as it is. - Repeat the process till at least two number is not divisible by any number except 1.The product of

the divisor and the undivided numbers is the required L.C.M.

**Example:**

**H.C.F. & L.C.M. of Fractions**

**L.C.M. = ^{L.C.M. of Numerator }/_{H.C.F. of Denominators}**

**Product of H.C.F. & L.C.M.**

H.C.F * L.C.M. = product of two numbers

**Decimal numbers**

L.C.M. of Decimal numbers

**Step 1.** Find the LCM of the given numbers without decimal.

**Step 2**.Put the decimal point ( in the LCM of Step 1) from right to left according to the MINIMUM decimal places among the given numbers..C.M. of Decimal numbers

**Comparison of Fractions:**

Find the L.C.M. of the denominators of the given fractions. Convert each of the fractions into an equivalent fraction with L.C.M as the denominator, by multiplying both the numerator and denominator by the same number. The resultant fraction with the greatest numerator is the greatest.