Exegesis:

hoi perioikoi lit. ‘those living around (her),’ ‘neighbours.’

hoi suggeneis autēs “her relatives” (An American Translation), cf. on v. 36.

hoti emegalunen kurios to eleos autou met’ autēs ‘that the Lord had made large his mercy with her,’ i.e. ‘dealt with her in a very merciful way’; for emegalunen cf. on v. 46; for to eleos cf. on v. 50. met’ autēs ‘with her,’ a Hebraism, means that she is the one to whom God’s mercy is directed.

kai sunechairon autē ‘and they were glad with her.’

sugchairō ‘to rejoice with someone,’ or ‘to congratulate’; here in the former meaning, and referring not only to inner feelings of joy and delight but also to their manifestation. The imperfect suggests duration as contrasted with the momentary aspect of the aorist of ēkousan.

Translation:

The first clause is sometimes better subordinated, e.g. ‘when her neighbours … heard that the Lord…, they rejoiced,’ ‘on hearing that the Lord…, her neighbours … rejoiced.’

Neighbours, or, ‘those who lived beside her’ (Apache), ‘those of the same street (or, ward),’ ‘co-villagers’ (Tae’), ‘people living-close-together around there’ (Toraja-Sa’dan), ‘the surrounding houses’ (Uab Meto), all implying a local relationship.

Kinsfolk, i.e. those of the same family or clan.

That the Lord had shown great mercy to her, or, ‘that the Lord had been very merciful towards her, or, had greatly mercy-ed her, or, had performed a very merciful deed for her’; cf. ‘that the Lord had made his mercy come so big over her’ (Sranan Tongo), ‘the Lord’s having been greatly kind to her’ (Navajo).

Rejoiced with her. The aspect is inceptive-durative, which in Marathi is expressed by the use of an inceptive imperfect form. Javanese has, ‘joined (in being) glad’ which says by implication only that they were glad with Elizabeth; Medumba uses a compound pronoun serving to refer to a combination of two groups or of an individual with a group: ‘they rejoiced they-plus-her (lit. they-with-they),’ which comes close to a reciprocal expression.

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.