7. A comet passes Earth every 70 years. Another comet passes Earth
every 75 years. If both comets pass Earth this year, how many years
will it be before they both pass Earth on the same year again?

1,050 years

Step-by-step explanation:

A comet passes Earth every 70 years.

Another comet passes Earth

every 75 years

If both comets pass Earth this year, how many years

will it be before they both pass Earth on the same year again?

Find the lowest common multiple of 70 years and 75 years

70 years = 70, 140, 210 , 280, 350, 420, 490, 560, 630, 700, 770, 840, 910, 980, 1050, 1120, 1190, 1260,

75 years = 75, 150, 225 , 300, 375, 450, 525, 600, 675, 750, 825, 900, 975, 1050, 1125, 1200, 1275, 1350

Lowest common multiple of 70 years and 75 years is 1,050 years

Therefore,

If both comets pass Earth this year, they both pass Earth the same year again in the next 1,050 years