Question
Tue April 21, 2015 By: Vaibhav Singh

Expert Reply
satyajit samal
Tue April 21, 2015
To find LCM or HCF of two or more than two numbers, we write them in prime factorised form.
3240 equals 2 cubed cross times 3 to the power of 4 cross times 5...... left parenthesis 1 right parenthesis 3600 equals 2 to the power of 4 cross times 3 squared cross times 5 squared...... left parenthesis 2 right parenthesis F i r s t space f i n d space t h e space L C M space o f space t h e s e space t w o space n u m b e r s. space T o space f i n d space L C M space comma space w e space t a k e space h i g h e s t space p o w e r s space o f space e a c h space p r i m e space n u m b e r space f r o m space t h e space g i v e n space t w o space n u m b e r s. H e n c e comma space L C M space o f space a b o v e space t w o space n u m b e r s equals 2 to the power of 4 cross times 3 to the power of 4 cross times 5 squared..... left parenthesis 3 right parenthesis S i n c e comma space t h e space p o w e r space o f space apostrophe 2 apostrophe space i n space 3600 space i s space apostrophe 4 apostrophe comma space t h e space L C M space w i l l space h a v e space a t l e a s t space p o w e r space o f space apostrophe 2 apostrophe space a s space apostrophe 4 apostrophe. space S o comma space a s s u m i n g space t h a t space t h e space q u e s t i o n space s t a t e s space t h a t space t h e space L C M space i s space 2 to the power of 4 cross times 3 to the power of 5 cross times 5 squared cross times 7 squared space f o r space t h r e e space n u m b e r s comma space w e space s o l v e space t h e space p r o b l e m. A l s o space g i v e n space t h a t space H C F space equals space 36 equals 2 squared cross times 3 squared...... left parenthesis 4 right parenthesis F r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space t h e space g i v e n space t w o space n u m b e r s space h a v e space p o w e r s space o f space apostrophe 2 apostrophe space a s space apostrophe 3 apostrophe space a n d space apostrophe 4 apostrophe. H e n c e comma space i f space H C F space h a s space 2 squared comma space t h e n space t h e space t h i r d space n u m b e r space s h o u l d space h a v e space 2 squared space i n space i t........ left parenthesis 5 right parenthesis S i m i l a r l y comma space c o n s i d e r i n g space t h e space p o w e r s space o f space apostrophe 3 apostrophe comma space L C M thin space h a s space p o w e r space apostrophe 5 apostrophe space a n d space H C F space h a s space p o w e r space a s space apostrophe 2 apostrophe. space S i n c e space w e space a l r e a d y space h a v e space 3 squared space i n space 3600 comma space t h e space H C F space c o n d i t i o n space i s space a l r e a d y space s a t i s f i e d. space B u t comma space f o r space t h e space L C M space t o space h a v e space 3 to the power of 5 comma space t h e space t h i r d space n u m b e r space m u s t space h a v e space 3 to the power of 5........ left parenthesis 6 right parenthesis space left parenthesis sin c e space t h e space o t h e r space t w o space n u m b e r s space d o space n o t space h a v e space p o w e r space o f space apostrophe 3 apostrophe space a s space apostrophe 5 apostrophe right parenthesis A l s o comma space sin c e space t h e space H C F space d o e s space n o t space h a v e space a n y space p o w e r space o f space apostrophe 5 apostrophe comma space t h e space t h i r d space n u m b e r space a l s o space s h o u l d space n o t space h a v e space a n y space p o w e r space o f space apostrophe 5 apostrophe..... left parenthesis 7 right parenthesis left parenthesis sin c e space t h e space o t h e r space t w o space n u m b e r s space a l r e a d y space h a v e space p o w e r s space o f space apostrophe 5 apostrophe right parenthesis F i n a l l y space t h e space L C M space h a s space 7 squared space i n space i t. space N o n e space o f space t h e space o t h e r space t w o space n u m b e r s space h a v e space 7 space a s space f a c t o r. space H e n c e comma space t h e space t h i r d space n u m b e r space s h o u l d space h a v e space 7 squared space i n space i t.... left parenthesis 8 right parenthesis S o space f r o m space left parenthesis 5 right parenthesis comma space left parenthesis 6 right parenthesis comma space left parenthesis 7 right parenthesis space a n d space left parenthesis 8 right parenthesis space w e space g e t space t h e space t h i r d space n u m b e r space i s space 2 squared cross times 3 to the power of 5 cross times 7 squared equals 47628
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