## H.C.F & L.C.M

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Notes On L.C.M and H.C.F

• 1
HOC. F & L.C Highest Common Factor Least Common multiple (L.C.m) Factors and multiple If a number A divides another number B exactly then we can say that A is Factor and B is multiple of A. 1. 2. 3. 4. multiple Part of Factor. It is definite. Exact to the number or less than this number. Greatest multiple of the number is itself. 1. 2. 3. 4. Factor It has multiple as part. It is indefinite. Exact to the number or greater Than this Number. Smallest factor of the number is Itself . H.C.F & L.c.m of Fractions H.C.F of Numerators I)H.C.F = L.C.M of Denomenators L.C.M of Numerators 2) L.c.m = H.C.F of Denomenators Product(multiplication) of two numbers is equal to product of their H.C.F & L.c.m. H.C.F of two prime numbers L.C.m of two prime numbers - their product. Find greatest value by which we divide X, Y, Z so remainder will be P,Q,R G.V = H.C.F of Find the greatest value by which we divide X, Y, Z so we get same remainder G.V = H.C.F of (X-Y),(Y-Z),(Z-X) Find lowest value by which we divide X, Y, Z so remainder will be P,Q,R [first take difference (X-P), and it will be same] L.V = L.c.m of (X, Y, Z) - difference Find the lowest value by which we divide X, Y, Z so we get same remainder L. V = L.C.m of (X, Y, Z) + remainder If two numbers given in ratio and H.C.F is also given then multiply H.C.F to these two numbers and you will get actual value. [For L.C.m you have to divide instead of multiplication]
• 2
H.C.F & L.C.m are given and one value is given then for find second value H.C.F*L.C.M Second value = one value Perfect number A number said to be perfect if the sum of all its divisor equal to this number. For find largest number of four digit exactly divisible by X, Y, Z. - First take largest number 9999 and take L.C.m of X, Y, Z. then Divide 9999 by L.C. m so we get remainder. so number will be = [9999-remainder] . For find smallest number of four digit exactly divisible by X, Y, Z. - First take largest number 9999 and take L.C.m of X, Y, Z. then Divide 9999 by L.C. m so we get remainder. so number will be = [leee+(L.C.m-Remainder)]. If L.C.M(/H.C.F) of number is given A. now a number by which A is not divisible. so it can't be their H.C.F(/L.C.m).

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