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Задать вопрос экспертам

Консультация № 195629

16.05.2019, 03:53

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Образование

Уважаемые эксперты! Пожалуйста, решить задачу: Разложением на простые множители найти наибольший общий делитель и наименьшее общее кратное чисел: 360 и 504. Проверить результат при помощи алгоритма Евклида и формулы наименьшего общего кратного.

Обсуждение

давно

Гордиенко Андрей Владимирович

Мастер-Эксперт
17387
18345

17.05.2019, 00:17

общий

это ответ

Здравствуйте, shinghalova!

360=2³*3²*5, 504=2³*3²*7,

поэтому

НОД(360, 504)=2³*3²=72, НОК(360, 504)=2³*3²*5*7=2520.

Вычислим НОД(360, 504), используя алгоритм Евклида.

504=360*1+144,

360=144*2+72,

144=72*2.

Поскольку последний ненулевой остаток равен 72, постольку НОД(360, 504)=72.

Вычислим НОД(360, 504), используя формулу наименьшего общего кратного.

НОД(360, 504)=360*504/(НОК(360, 504))=2³*3²*5*2³*3²*7/(2³*3²*5*7)=2³*3²=8*9=72.

Об авторе:
Facta loquuntur.

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