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Determine the least number which when divided by 3, 4 and 5 leaves remainder 2 in each case.

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#### Solution

We have,

2 |
3, 4, 5 |

2 |
3, 2, 5 |

3 |
3, 1, 5 |

5 |
1, 1, 5 |

1, 1, 1 |

Since, the LCM of 3, 4 and 5 is 2 × 2 × 3 × 5 = 60.

∴ The required number is 6 is the least number which when divided by 3, 4 and 5 leaves remainder 2 in each case.

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