Question

Q6. Find the least number which when divide by 15,18 and 25 leaves a remainder 4
in each case.​

Answer 1

Answer:

454

Step-by-step explanation:

this is the right answer

Answer 2

x≡4(mod16)x≡4(mod16)

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)x≡4(mod20)x≡4(mod20)

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)x≡4(mod20)x≡4(mod20)x≡4(mod25)x≡4(mod25)

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)x≡4(mod20)x≡4(mod20)x≡4(mod25)x≡4(mod25)16=2416=24

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)x≡4(mod20)x≡4(mod20)x≡4(mod25)x≡4(mod25)16=2416=2418=2×3218=2×32

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)x≡4(mod20)x≡4(mod20)x≡4(mod25)x≡4(mod25)16=2416=2418=2×3218=2×3220=22×520=22×5

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)x≡4(mod20)x≡4(mod20)x≡4(mod25)x≡4(mod25)16=2416=2418=2×3218=2×3220=22×520=22×525=5225=52

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)x≡4(mod20)x≡4(mod20)x≡4(mod25)x≡4(mod25)16=2416=2418=2×3218=2×3220=22×520=22×525=5225=52L.C.M. (16, 18, 20, 25)=24×32×52=3600L.C.M. (16, 18, 20, 25)=24×32×52=3600

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)x≡4(mod20)x≡4(mod20)x≡4(mod25)x≡4(mod25)16=2416=2418=2×3218=2×3220=22×520=22×525=5225=52L.C.M. (16, 18, 20, 25)=24×32×52=3600L.C.M. (16, 18, 20, 25)=24×32×52=3600∴3600 is the least number which will leave no remainder when∴3600 is the least number which will leave no remainder when

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)x≡4(mod20)x≡4(mod20)x≡4(mod25)x≡4(mod25)16=2416=2418=2×3218=2×3220=22×520=22×525=5225=52L.C.M. (16, 18, 20, 25)=24×32×52=3600L.C.M. (16, 18, 20, 25)=24×32×52=3600∴3600 is the least number which will leave no remainder when∴3600 is the least number which will leave no remainder whendivided by 16, 18, 20 and 25.divided by 16, 18, 20 and 25.

x≡4(mod16)x≡4(mod16)x≡4(mod18)x≡4(mod18)x≡4(mod20)x≡4(mod20)x≡4(mod25)x≡4(mod25)16=2416=2418=2×3218=2×3220=22×520=22×525=5225=52L.C.M. (16, 18, 20, 25)=24×32×52=3600L.C.M. (16, 18, 20, 25)=24×32×52=3600∴3600 is the least number which will leave no remainder when∴3600 is the least number which will leave no remainder whendivided by 16, 18, 20 and 25.divided by 16, 18, 20 and 25.∴3604 will be the least number