# HCF & LCM Maths Study Materials | Quantitative Aptitude

Factors and Multiples

• If number adivided another number b exactly, we say that a is a factor of b.
• In this case, bis 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 = 22✘33, 288 = 25✘32 and 360 = 23✘5✘32

H.C.F. = 22✘32=36

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.

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